Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 7 - Exponents and Exponential Functions - 7-3 Multipying Powers with the Same Base - Practice and Problem-Solving Exercises - Page 429: 23



Work Step by Step

We start with the given expression: $(x^5y^2)(x^{-6}y)$ We rearrange and regroup the expression using the associative and commutative properties of multiplication: $(x^5x^{-6})(y^2y)$ To multiply powers with the same base, we add the exponents: $(x^{5+(-6)})(y^{2+1})=x^{-1}y^3$ The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this rule to rewrite the expression: $\frac{y^3}{x}$
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