Algebra 1

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

Chapter 7 - Exponents and Exponential Functions - 7-4 More Multiplication Properties of Exponents - Practice and Problem-Solving Exercises - Page 436: 20



Work Step by Step

We start with the given expression: $(t^2)^{-2}(t^2)^{-5}$ We simplify according to the order of operations: First, we simplify powers: To raise a power to a power, we multiply the exponents: $t^{2\times-2}t^{2\times-5}=t^{-4}t^{-10}$ Next, we multiply. To multiply powers with the same base, we add the exponents. $t^{-14}$ 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: $\frac{1}{t^{14}}$
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