Write with Rational (Fractional) Exponents ( fourth root of -y)^4

${(\sqrt[4]{- y})}^{4}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{- y}$ as ${(- y)}^{\frac{1}{4}}$ .

${({(- y)}^{\frac{1}{4}})}^{4}$

Multiply the exponents in ${({(- y)}^{\frac{1}{4}})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(- y)}^{\frac{1}{4} \cdot 4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(- y)}^{\frac{1}{4} \cdot 4}$

Rewrite the expression.

${(- y)}^{1}$

Simplify.

$- y$