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: 27

Answer

$\frac{1}{8y^{12}}$

Work Step by Step

We start with the given expression: $(2y^{4})^{-3}$ To raise a product to a power, we raise each factor to the power and multiply: $2^{-3}(y^{4})^{-3}$ To raise a power to a power, we multiply the exponents: $2^{-3}y^{-12}$ 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: $\frac{1}{2^3y^{12}}$ We expand the exponent in the denominator: $\frac{1}{2^3y^{12}}=\frac{1}{2\times2\times2y^{12}}=\frac{1}{8y^{12}}$
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