Solve for y fourth root of y=-4

$\sqrt[4]{y} = - 4$

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

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

Simplify each side of the equation.

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

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

Simplify the left side.

Simplify ${(y^{\frac{1}{4}})}^{4}$ .

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$y^{1} = {(- 4)}^{4}$

Simplify.

$y = {(- 4)}^{4}$

Simplify the right side.

Raise $- 4$ to the power of $4$ .

$y = 256$

Exclude the solutions that do not make $\sqrt[4]{y} = - 4$ true.

$No solution$