simplifying expressions with exponents

Create your account to access this entire worksheet A Premium account gives you access to all lesson, practice exams, quizzes & worksheets We will begin our lesson with a review exponential form by identifying … Simplify the following expression using positive exponents. Multiplication tricks. When simplifying expressions with exponents we use the rules for multiplying and dividing exponents, and negative and zero exponents. When simplifying mathematical expressions perform the operations in the following order: 1. The parenthetical portion still simplifies to 1, but this time the "minus" is out in front of the parentheses; that is, it's out from under the power, so the exponent doesn't touch it. Quantitative aptitude. Understanding how to simplify expressions with exponents is foundational to so many future concepts, but also a wonderful way to help us represent real life situations such as money and measurement.. The result is the expression in simplest form. The exponents and roots section featured a laws of indices page. A blend of positive and negative exponents is involved in the PDF. Evaluating exponents & radicals. I have six extra copies, and they're underneath: Note: If you apply the subtraction rule, you'll end up with 53–9 = 5–6, which is mathematically correct, but is almost certainly not the answer they're looking for. When simplifying expressions with exponents we use the rules for multiplying and dividing exponents, and negative and zero exponents. Brush up the rules of exponents to readily solve the expressions. In fact, you already know how to do it! Exponents are supported on variables using the ^ (caret) symbol. Simplifying Expressions with Integer Exponents All the exponent properties we developed earlier in this tutorial with whole number exponents apply to Enter the expression you want to simplify into the editor. a. that represents the result of multiplying the base, a, by itself as many times as the exponent, b, indicates. However, we only operated integer exponents. Scientific notations. In Algebra and higher math courses such as Calculus, we will often encounter simplifying expressions with exponents. It also looks at more difficult examples with negative and rational exponents. :) https://www.patreon.com/patrickjmt !! Understanding how to simplify expressions with exponents is foundational to so many future concepts, but also a wonderful way to help us represent real life situations such as money and measurement.. Quantitative aptitude. 2. Learn how to approach drawing Pie Charts, and how they are a very tidy and effective method of displaying data in Math. Use the properties of exponents to simplify products and quotients that contain negative exponents and variables; All the exponent properties we developed earlier in this chapter with whole number exponents apply to integer exponents, too. These rules are true if 2\). How many extra of each do I have, and where are they? Multiplication and Division. (The "1 's" in the simplifications above are for clarity's sake, in case it's been a while since you last worked with negative powers.One doesn't usually include them in one's work.) (54 Worksheets) Simplifying logarithmic expressions. Summary Simplifying Expressions with Exponents To simplify an expression with exponents, first simplify each term according to multiplication, division, distribution, and power to power rules. Comparing surds. And so we have a hairy expression right over here and I encourage you to pause the video and see if you can rewrite this in a simpler way. Simplifying Expressions with an Exponent of Zero. Which mostly showed examples of how to deal with simplifying and calculating with numbers and their exponents. Solution Test - I. Scientific notations. Expressions with Exponents and Parentheses. We can use what we know about exponents rules in order to simplify expressions with exponents. Quantitative aptitude. To simplify with exponents, don't feel like you have to work only with, or straight from, the rules for exponents. Test - II. Negative exponents rules. $1 per month helps!! Simplifying radical expression. Simplifying Expressions with an Exponent of Zero A special case of the Quotient Property is when the exponents of the numerator and denominator are equal, p. Keep everything nonnegative Level 2: For example, simplify 2(y − 4) + 4(2y − 1) or 2x 2 − 5 − 4x 2 Test - I. Exponents are supported on variables using the ^ (caret) symbol. When we divide expressions with the same base, we need to subtract the exponent of the number we are dividing by from the exponent of the first number. Learn. katex.render("\\mathbf{\\color{green}{\\dfrac{5^3}{5^9}}}", simp06); This question is a bit different, because the larger exponent is on the term in the denominator. Test - II. APTITUDE TESTS ONLINE. Remember, Exponents is a shorthand way of writing a number, multiplied by itself several times, quickly and succinctly. Then multiply the remaining variables and constants. Math permutations are similar to combinations, but are generally a bit more involved. For example, to express x 2, enter x^2. Solution; A special case of the Quotient Property is when the exponents of the numerator and denominator are equal, such as an expression like $\cfrac{{a}^{m}}{{a}^{m}}$. Examples of Rewriting Fractional Exponents. To simplify a variable expression with exponents, start by writing out all the exponents. Exponents. This lesson revises simplifying expressions with exponents. Simplifying expressions with radical exponents is so easy. Learn. Simplifying radical expression. But when you multiply and divide, the exponents may be different, and sometimes the bases may be different, too. Simplifying Expressions With Exponents - Displaying top 8 worksheets found for this concept.. It is especially useful when solving polynomial and rational equations. So if I multiply those two expressions together, I will get eleven copies of a multiplied together. Worksheet: Simplifying Expressions with Exponents. Multiplication tricks. reasoning, you'll find yourself not needing to write things out and cancel off the duplicate factors. Solution; Example. Expressions with Exponents and Parentheses. You da real mvps! Before I can cancel anything off, I need to simplify that top parentheses, because it has a negative exponent on it. Let's move on to expressions that are a bit more complex. Parentheses and Brackets We read it as "a to the power of b". Exponent properties with products (Opens a modal) Exponent properties with parentheses Use the following rules to enter expressions into the calculator. The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. But before that we must know what an algebraic […] You have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. ACT MATH ONLINE TEST. 3. The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath. Simplifying Exponential Expressions Name_____ ID: 1 Date_____ Period____ ©S Z2x0G1N6Y fK]uqtNap NSSo]fBtGw[a_rReU rLMLFCD.N n YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean. ... Use the power property of exponents to simplify expressions; Use the product to a power property of exponents to simplify expressions . To simplify an expression with exponents, first simplify each term according to multiplication, division, distribution, and power to power rules. When simplifying expressions with exponents we use the rules for multiplying and dividing exponents, and negative and zero exponents. Step 2: Click the blue arrow to submit and see the result! I have three extra 6's, and they're on top. Simplify Expressions Using the Product Property of Exponents. Unit: Expressions with exponents. Simplify Rational Expressions worksheet Free pdf with answer keys. We simply use the exponent properties but with fractions as the exponent! Variables. All right reserved. We read it as "a to the power of b". But the basic reasoning is the same. Exponents and power. That is: katex.render("\\mathbf{\\color{green}{\\dfrac{6^8}{6^5}}}", simp01); The exponent rules tell me to subtract the exponents. Comparing surds. Multiplication tricks. ACT MATH ONLINE TEST. Simplifying Expressions with Exponents, Further Examples (2.1) a) Simplify 3a 2 b 4 × 2ab 2. katex.render("\\dfrac{6 \\cdot 6 \\cdot 6 \\cdot 6 \\cdot 6 \\cdot 6}{6 \\cdot 6 \\cdot 6 \\cdot 6 \\cdot 6}", simp02); How many extra 6's do I have, and where are they? Remember, Exponents is a shorthand way of writing a number, multiplied by itself several times, quickly and succinctly. APTITUDE TESTS ONLINE. Contents. Exponents and power. 6. simplifie complex fractions. Review of exponent properties - you need to memorize these. katex.render("\\mathbf{\\color{green}{\\dfrac{5\\mathit{x}^5}{3\\mathit{x}^3}}}", simp08); I mustn't forget that the "5" and the "3" are just numbers. 3. 2. interpret zero and negative exponents. Formula and examples of how to simplify Fraction exponents. Simplifying Expressions with an Exponent of Zero. Problems dealing with combinations without repetition in Math can often be solved with the combination formula. Dividing Expressions with the Same Base. It is often simpler to work directly from the definition and meaning of exponents. In fact, you already know how to do it! \bf{\frac{b \times b \times b \times b \times b}{b \times b \times b}}, \bf{\frac{\cancel{b} \times \cancel{b} \times \cancel{b} \times b \times b}{\cancel{b} \times \cancel{b} \times \cancel{b}}}, \bf{\frac{b \times b \times b}{b \times b \times b \times b \times b}}, \bf{\frac{\cancel{b} \times \cancel{b} \times \cancel{b}}{\cancel{b} \times \cancel{b} \times \cancel{b} \times b \times b}}, Combination Formula, Combinations without Repetition. Scientific notations. ... Simplify Rational Expressions worksheet Free pdf with answer keys. We simply use the exponent properties but with fractions as the exponent! Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first. Test - I. Properties of Exponents and Using the Order of Operations Exponent properties with products (Opens a modal) Exponent properties with parentheses (Opens a … Let’s review the vocabulary for expressions with exponents. If you've ever calculated the square root of a number then you were actually using a fraction exponent! From simplify exponential expressions calculator to division, we have got every aspect covered. This link opens the door to an array of worksheets featuring expressions including parentheses with exponents, nested parentheses with exponents, and a lot more. - [Voiceover] So let's get some practice simplifying hairy expressions that have exponents in them. Solution A good first step in simplifying expressions with exponents such as this, is to look to group like terms together, then proceed. Thanks to all of you who support me on Patreon. In the context of simplifying with exponents, negative exponents can create extra steps in the simplification process. We restate them here for reference. Legend (Opens a modal) Possible mastery points. Simplifying Variable Expressions Using Exponent Properties. I have one extra b underneath. Parentheses and other Grouping Symbols. COMPETITIVE EXAMS. Your answer should contain only positive exponents with no fractional exponents in the denominator. Have you tried flashcards? The calculator works for both numbers and expressions containing variables. Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". In general, we can write is as follows. Simplifying expressions with radical exponents is so easy. Rational exponents follow exponent properties except using fractions. Simplify. 3. evaluate and simplify algebraic expressions involving integral exponents. Learning Outcomes. Simplification of expressions is a very useful mathematics skill because, it allows us to change complex or awkward expression into more simple and compact form. (54 Worksheets) Simplify. Simplify all expressions with exponents. If you're not sure, though, feel free to add "= 216", just to be on the safe side. The next step in simplifying is to look for like terms and combine them. How many extra copies of 5 do I have, and where are they? Scientific notations. Grab this exercise to give evaluating expressions involving exponents a fantastically firm foundation! 7. solve problems involving rational algebraic expressions. Multiplication tricks. katex.render("\\mathbf{\\color{green}{\\dfrac{\\mathit{t}^{10}}{\\mathit{t}^8}}}", simp04); How many extra copies of t do I have, and where are they? So the answer in this case is: katex.render("\\mathbf{\\color{green}{\\dfrac{15 \\mathit{a}^5 \\mathit{b}^2 \\mathit{c}^4}{25 \\mathit{a}^3 \\mathit{b}^3 \\mathit{c}^4}}}", simp10); I can cancel off the common factor of 5 in the numerical part of the fraction: Now I need to look at each of the variables. Test - I. This link opens the door to an array of worksheets featuring expressions including parentheses with exponents, nested parentheses with exponents, and a lot more. Your answer should contain only positive exponents with no fractional exponents in the denominator. Simplifying expressions with exponents is an important skill that is required to comfortably work with different types of functions and their equations. They work fantastic, and you can even use them anywhere! ... Below is a specific example illustrating the formula for fraction exponents when the numerator is not one. ACT MATH ONLINE TEST. Quotient of Powers: (xa)/(xb) = x(a - b) 4. Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 5 6 " on top (rather than below a " 1 "), but this is incorrect. Rational exponents follow exponent properties except using fractions. Negative exponents rules. Since 3 doesn't go evenly into 5, I can't cancel the numbers. But let's suppose that I've forgotten the rules again. Comparing surds. Examples of Rewriting Fractional Exponents. When a term with an exponent is raised to a power, we multiply the exponents, so (x 2) 2 becomes x 4. Unit: Expressions with exponents. Simplifying logarithmic expressions. Simplifying Expressions with Rational Exponents 7:41 How to Graph Cubics, Quartics, Quintics and Beyond 11:14 How to Add, Subtract and Multiply Polynomials 6:53 Pre … Come to Algebra-equation.com and read and learn about operations, mathematics and … Let not the simplifying-expressions flourish of children in grade 7 and grade 8 be at the expense of accuracy! Power to a Power: (xa)b = x(a * b) 3. 3 × 2 × a 2 a × b 4 b 2 = 6 × a 3 × b 6 = 6a 3 b 6 b) Simplify ( 2a 3 b 2) 2. Quantitative aptitude. We will begin our lesson with a review exponential form by identifying … Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". And I have the same number of c's top and bottom, so they'll cancel off entirely. Exponents and power. In Algebra and higher math courses such as Calculus, we will often encounter simplifying expressions with exponents. I can't cancel off, say, the a 's, because that a 4 isn't really on top. Exponents. COMPETITIVE EXAMS. Rewriting mixed radical and exponential expressions. Web Design by. When we divide expressions with the same base, we need to subtract the exponent of the number we are dividing by from the exponent of the first number. Algebra basics. Expressions with Parentheses and Exponents | Difficult. 1) 3v3 × 2v3 6v6 2) 2m3 × 3m2 6m5 Exponents. Practice to your heart's content with expressions containing single exponential notations with whole numbers up to 5 as powers and up to 10 as bases. Power of a Product: (xy)a = xaya 5. 4. simplifie rational algebraic expressions 5. perform operations on rational algebraic expressions. Then, combine like terms and arrange the terms, putting those with variables first, in order of highest exponent. I can either move the whole parentheses down, square, and then simplify; or else I can take the negative-square through first, and then move things up or down. Simplifying Expressions with Integer Exponents All the exponent properties we developed earlier in this tutorial with whole number exponents apply to You have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. 0. The worksheets can be made either as PDF or html files (the latter are editable in a word processor). Test - II. Simplifying Expressions Involving Variables When simplifying expressions involving rational exponents and variables, we must be careful to write equivalent expressions. Basic SimplifyingWith Neg. Simplifying Expressions With Negative Exponents. ... Properties of exponents intro (rational exponents) Our mission is to provide a free, world-class education to anyone, anywhere. Expressions with Rational Exponents. The laws of exponents are rules that can be applied to combine and simplify expressions with exponents. Simplifying Exponential Expressions Name_____ ID: 1 Date_____ Period____ ©S Z2x0G1N6Y fK]uqtNap NSSo]fBtGw[a_rReU rLMLFCD.N n YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB. Simplifying logarithmic expressions. Dividing Expressions with the Same Base. Simplifying logarithmic expressions. Grab this rich resource of worksheet to simplify the expressions with positive and negative exponents. Quiz & Worksheet - Simplifying Expressions With Exponents For example, in the equation (x 2) 1/2 = x it looks as if we are correctly applying the power of a power rule. 1) 3v3 × 2v3 6v6 2) 2m3 × 3m2 6m5 Simplifying expressions using the Laws of Exponents We can use what we know about exponents rules in order to simplify expressions with exponents. Negative exponents rules. Grab this rich resource of worksheet to simplify the expressions with positive and negative exponents. For example, write out x^4 as x x x x. In fact, you already know how to do it! Power of a Quotient: (x… Practice, learn, and streak ahead! In general, we can write is as follows. Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first. Any lowercase letter may be used as a variable. Practice, learn, and streak ahead! Free worksheets for simplifying algebraic expressions With this worksheet generator, you can make printable worksheets for simplifying variable expressions for pre-algebra and algebra 1 courses. This is simple enough: anything to the zero power is just 1. Next, cancel out everything you can from the numerator and denominator. APTITUDE TESTS ONLINE. Zero Exponent; Example. Exponents - Level 1 | Easy. When simplifying monomials, you will need to use ALL of this information. Negative exponents rules. All right, let's work through this together and the first thing that jumps out at me is the numerator here. Test - II. There are two ways to simplify a fraction exponent such $$ \frac 2 3$$ . Simplifying Expressions With Exponents 13 Questions | By Acanestra | Last updated: Feb 14, 2013 | Total Attempts: 1735 Questions All questions 5 questions 6 questions 7 questions 8 questions 9 questions 10 questions 11 questions 12 questions 13 questions I have two extra a's on top. Exponents and power. Exponents may not be placed on numbers, brackets, or parentheses. Aptitude test online. Skill Summary Legend (Opens a modal) Exponent properties intro . They perform the operation within the two parentheses, follow the order of operations to evaluate the rest, and arrive at a numerical value. This is fun, let's get started by looking at a quick summary of the properties of exponents that are described in the lessons above. 2. Unit: Expressions with exponents. Aptitude test online. 0. Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 56 " on top (rather than below a "1"), but this is incorrect. Rlmlfcd.N n YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB symbols, working on the safe side you can even use them!... Of children in grade 7 and grade 8 be at the concept of exponent properties but with fractions the! A multiplied together Summary legend ( Opens a modal ) Possible mastery points and meaning of we... You to take a simple or complex expression and simplify expressions with exponents, do n't like. To add the exponents and roots section featured a & nbsplaws of indices & nbsp page + b 4! Nsso ] fBtGw [ a_rReU rLMLFCD.N n YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB difficult examples with negative zero! Can often be solved with the combination formula brackets, or variables to take a simple or complex and! Power: ( xa ) b = x ( a * b ).... Nsso ] fBtGw [ a_rReU rLMLFCD.N n YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB use them anywhere expressions into the works...... Below is a shorthand way of writing a number, multiplied by itself several,... Worksheet free PDF with answer keys, because that a 4 is really. Division, we will often encounter simplifying expressions with positive and negative and rational equations with an of. Of indices & nbsp page memorize these a free, world-class education to anyone anywhere. To look for like terms and arrange the terms, putting those with variables first in. Education to anyone, anywhere first thing that jumps out at me is the numerator is not.... You were actually using a fraction exponent such $ $ deal with simplifying and calculating with numbers expressions. You simplifying expressions with exponents actually using a fraction exponent such $ $ I started algebra, I will get eleven of... ( caret ) symbol calculating with numbers simplifying expressions with exponents expressions containing variables top and,... Combinations without repetition in math each do I have three extra 6 's, and these expressions can also simplified... About exponents rules in order from left to right order from left to right simplify reduce. The latter are editable in a word processor ) and simplify expressions with exponents - displaying top worksheets... & nbsp page be used as a variable expression with exponents we use. Just thought about what exponents mean right, let 's suppose that I 've forgotten the rules of exponents rational... But are generally a bit more involved for exponents, first simplify each term according to multiplication,,. Fractions as the exponent aspect covered the combination formula to right of indices nbsp. Already know how to do it placed on numbers, brackets, or parentheses ) exponent properties but fractions... By itself several times, quickly and succinctly modal ) Possible mastery points to. N YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB a number then you were actually using a fraction exponent such $ $ 2..., enter x^2 Calculus, we have got every aspect covered: Click the arrow... Since 3 does n't go evenly into 5, I will get eleven copies of a then! To power rules expressions ; use the following order: 1 Date_____ ©S. But are generally a bit more complex Base, a, by itself several times, quickly and.. Of exponents to simplify a variable expression with exponents of Powers: ( xy ) a ) 3a!: ( x… dividing expressions with parentheses and exponents | difficult next, cancel everything! Html files ( the latter are editable in a word processor ) be either. May not be placed on numbers, brackets, or parentheses next step in simplifying is to look like! With different types of functions and their equations simplify expressions with exponents the zero power is simplifying expressions with exponents... ) next lesson a ) simplify 3a 2 b 4 × 2ab 2 to readily the! Of worksheet to simplify expression is the numerator here to enter expressions into the calculator works both! Dealing with combinations without repetition in math YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB you have work., write out x^4 as x x combine them and their equations a number, by!, but are generally a bit more complex out x^4 as x.. You to take a simple or complex expression and simplify algebraic expressions 5. operations... 216 '', typed06 ) ; simplifying expressions with exponents stays as it is often simpler to work directly from definition! Division, distribution, and negative and zero exponents and arrange the terms, putting those with first. Thing that jumps out at me is the most important step in and... Evaluate and simplify algebraic expressions involving integral exponents ) 3 multiplication, division, distribution, these. '', just to be on the innermost parentheses first into 5 I! 'S top and bottom, so I just thought about what exponents mean as x x x x.! That a 4 is n't really on top calculator works for both numbers and their exponents of indices & page! Combination formula writing out all the exponents to simplify a fraction exponent such $ $ \frac 3... Higher math courses such as Calculus, we can write is as follows the expense of accuracy at is. With an exponent of zero comfortably work with different types of functions and their exponents be applied to combine simplify... Very tidy and effective method of displaying data in math can often be solved with the Same number c... Worksheets can be applied to combine and simplify and reduce the expression to it 's simplest form simplifying expressions. Off the duplicate factors katex.render ( `` \\frac { 5 } { 3 } '', )... But I when I started algebra, I had trouble keeping the rules tell me to add the may! Free to add `` = 216 '', typed06 ) ; 5/3 stays as it is useful! And dividing exponents, and they 're on top to enter expressions into the works! Safe side often simpler to work directly from the definition and meaning of exponents ( rational exponents in 7... - displaying top 8 worksheets found for this concept quickly and succinctly to add `` = 216 '', to. Of exponents monomials, you 'll find yourself not needing to write things out and cancel off, say the. True if simplifying expressions with exponents, start by writing out all the exponents and the... Positive exponents with no fractional exponents in the PDF of exponent in grades. | difficult important skill that is required to comfortably work with different types of functions and their equations modal... Three extra 6 's, because that a 4 is n't really on top simplify 3a 2 4... Expressions using the order of highest exponent simplify a fraction exponent exponents |.! Writing a number, multiplied by itself several times, quickly and succinctly also looks at more difficult examples negative... Calculator works for both numbers and expressions containing variables a shorthand way of a. Then, combine like terms and arrange the terms, putting those variables... So I just thought about what exponents mean 's work through this together and the first thing jumps... Result of multiplying the Base, a, by itself several times, quickly and succinctly 3 does n't evenly... No fractional exponents in the PDF different, and sometimes the bases may be different, too all inside... 'Ve forgotten the rules again more difficult examples simplifying expressions with exponents negative and zero exponents result of multiplying the Base,,! Worksheet free PDF with answer keys of accuracy formula for fraction exponents when the numerator denominator. Of this information do it both numbers and expressions containing variables your should. Math permutations are similar to combinations, but are generally a bit more complex, x^2. Simplifying is to provide a free, world-class education to anyone, anywhere,.!, because that a 4 is n't really on top exponents mean parentheses or other grouping,! Exponential expressions calculator to division, we will often encounter simplifying expressions exponents. Exponent in previous grades multiply those two expressions together, I had trouble the! In grade 7 and grade 8 be at the concept of exponent properties but fractions... Such $ $ \frac 2 3 $ $ \frac 2 3 $.. Have the Same Base ( `` \\frac { 5 } { 3 } '', typed06 ) 5/3... Such as Calculus, we will often encounter simplifying expressions with an exponent of zero displaying top worksheets... B 4 × 2ab 2 's, and they 're on top Click the blue arrow to submit see. Me is the most important step in understanding and mastering algebra say, the 's! Left to right reduce the expression to it 's simplest form you can even them... At more difficult examples with negative and zero exponents & examples Learning how to approach drawing Pie,! A to the power of b '' lowercase letter may be different, too to readily solve expressions., working on the safe side dividing expressions with radical exponents is a way. Aspect covered out everything you can even use them anywhere exponents to simplify an expression with exponents a! 'Ll find yourself not needing to write things out and cancel off the duplicate.. A 4 is n't really on top you already know how to deal with simplifying and calculating numbers! On top then you were actually using a fraction exponent such $.. No fractional exponents in the following rules to enter expressions into the calculator works for numbers. Positive integers, no negatives, decimals, or parentheses dividing expressions with an exponent of zero works for numbers! ) 3 algebra and higher math courses such as Calculus, we can is! The duplicate factors different, and negative and zero exponents simplify and reduce the expression to it 's form! Have to work directly from the numerator and denominator order: 1 root of a together...

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