## College Algebra (6th Edition)

$16y^\frac{1}{2}$
$$\frac{(2y^\frac{1}{5})^4}{y^\frac{3}{10}}$$ 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: $$=16y^\frac{1}{2}$$