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.3: 100

Answer

$16y^\frac{1}{2}$

Work Step by Step

$$\frac{(2y^\frac{1}{5})^4}{y^\frac{3}{10}}$$ When an exponential expression is raised to a power, multiply the exponents: $$=\frac{16y^{(\frac{1}{5}\times4)}}{y^\frac{3}{10}}$$ $$=\frac{16y^\frac{4}{5}}{y^\frac{3}{10}}$$ To divide exponential expressions with the same base, subtract the exponent of the denominator from the exponent of the numerator: $$=16y^{(\frac{4}{5}-\frac{3}{10})}$$ To subtract fractions, convert the fractions so they have a common denominator: $$=16y^{(\frac{8}{10}-\frac{3}{10})}$$ $$=16y^\frac{5}{10}$$ Simplify all fractions: $$=16y^\frac{1}{2}$$
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