Algebra Examples

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

Step 1

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

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

Step 2

Simplify each side of the equation.

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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Step 2.2.1.1.1

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

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

Step 2.2.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

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

Step 2.2.1.1.2.2

Rewrite the expression.

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

Step 2.2.1.2

Simplify.

$j = 4^{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$j = 256$