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: 59

Answer

$=\frac{y^{2}}{25x^{6}}$

Work Step by Step

$$(\frac{5x^{3}}{y})^{-2}$$ When raising a quotient to a power, raise both the numerator and denominator to the power: $$=\frac{(5x^{3})^{-2}}{y^{-2}}$$ When raising a product to a power, raise each factor to that power: $$=\frac{5^{-2}x^{(3\times(-2)}}{y^{-2}}$$ $$=\frac{5^{-2}x^{-6}}{y^{-2}}$$ Move the base with the negative exponent to the other side of the fraction, and make the exponent positive: $$=\frac{y^{2}}{5^{2}x^{6}}$$ $$=\frac{y^{2}}{25x^{6}}$$
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