Solve for j fourth root of j=5

$\sqrt[4]{j} = 5$

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

${\sqrt[4]{j}}^{4} = 5^{4}$

Simplify each side of the equation.

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

${(j^{\frac{1}{4}})}^{4} = 5^{4}$

Simplify the left side.

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

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

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

$j^{\frac{1}{4} \cdot 4} = 5^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$j^{\frac{1}{4} \cdot 4} = 5^{4}$

Rewrite the expression.

$j^{1} = 5^{4}$

Simplify.

$j = 5^{4}$

Simplify the right side.

Raise $5$ to the power of $4$ .

$j = 625$