Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - 6-4 Rational Exponents - Practice and Problem-Solving Exercises - Page 387: 70

Answer

$-3$

Work Step by Step

We want to break down this problem a little to be able to work with it. The number $-243$ can be broken down into a small base raised to a power: $(-3)^5$. Let's rewrite this number: $(-3^5)^{1/5}$ Raising a power to a power means we can multiply the two powers or exponents together: $-3^{(5)(1/5)}$ Multiply to simplify: $-3^{(5/5)}$ Reduce the fraction in the exponent by dividing both numerator and denominator by $5$, the greatest common factor: $-3^{(1)}$ When we raise a number to the power of $1$, then the number can just be written as the base without an exponent: $-3$
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