Algebra 1

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

Chapter 7 - Exponents and Exponential Functions - 7-1 Zero and Negative Exponents - Practice and Problem-Solving Exercises - Page 418: 39



Work Step by Step

We rewrite the given expression as a division problem: $3r\div s^{-2}$ 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: $3r\div\frac{1}{s^2}$ To divide by a fraction, we multiply by the reciprocal: $3r\times s^2$ We plug in the values for $r$ and $s$: $3(-3)\times5^2$ The order of operations states that first we perform operations inside grouping symbols, such as parentheses, brackets, and fraction bars. Then, we simplify powers. Then, we multiply and divide from left to right. We follow the order of operations to simplify: First, we simplify powers: $3(-3)\times25$ Then, we multiply from left to right: $-9\times25=-225$
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