College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.2: 60

Answer

$\frac{y^{3}}{27x^{12}}$

Work Step by Step

$$(\frac{3x^{4}}{y})^{-3}$$ When raising a quotient to a power, raise both the numerator and denominator to the power: $$=\frac{(3x^{4})^{-3}}{y^{-3}}$$ When raising a product to a power, raise each factor to that power: $$=\frac{3^{-3}x^{(4\times(-3))}}{y^{-3}}$$ $$=\frac{3^{-3}x^{-12}}{y^{-3}}$$ Move the base with the negative exponent to the other side of the fraction, and make the exponent positive: $$=\frac{y^{3}}{3^{3}x^{12}}$$ $$=\frac{y^{3}}{27x^{12}}$$
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