Solve for u fourth root of u=2

$\sqrt[4]{u} = 2$

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

${\sqrt[4]{u}}^{4} = 2^{4}$

Simplify each side of the equation.

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

${(u^{\frac{1}{4}})}^{4} = 2^{4}$

Simplify the left side.

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

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

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

$u^{\frac{1}{4} \cdot 4} = 2^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$u^{\frac{1}{4} \cdot 4} = 2^{4}$

Rewrite the expression.

$u^{1} = 2^{4}$

Simplify.

$u = 2^{4}$

Simplify the right side.

Raise $2$ to the power of $4$ .

$u = 16$