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