Simplify cube root of (y^2)/(y^(4/5))

$\sqrt[3]{\frac{y^{2}}{y^{\frac{4}{5}}}}$

Reduce the expression by cancelling the common factors.

Move $y^{\frac{4}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\sqrt[3]{y^{2} y^{- \frac{4}{5}}}$

Multiply $y^{2}$ by $y^{- \frac{4}{5}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[3]{y^{2 - \frac{4}{5}}}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\sqrt[3]{y^{2 \cdot \frac{5}{5} - \frac{4}{5}}}$

Combine $2$ and $\frac{5}{5}$ .

$\sqrt[3]{y^{\frac{2 \cdot 5}{5} - \frac{4}{5}}}$

Combine the numerators over the common denominator.

$\sqrt[3]{y^{\frac{2 \cdot 5 - 4}{5}}}$

Simplify the numerator.

Multiply $2$ by $5$ .

$\sqrt[3]{y^{\frac{10 - 4}{5}}}$

Subtract $4$ from $10$ .

$\sqrt[3]{y^{\frac{6}{5}}}$

Rewrite $y^{\frac{6}{5}}$ as ${(y^{\frac{2}{5}})}^{3}$ .

$\sqrt[3]{{(y^{\frac{2}{5}})}^{3}}$

Pull terms out from under the radical, assuming real numbers.

$y^{\frac{2}{5}}$