Algebra Examples

$\sqrt[4]{v} = 3$

Step 1

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

${\sqrt[4]{v}}^{4} = 3^{4}$

Step 2

Simplify each side of the equation.

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

${(v^{\frac{1}{4}})}^{4} = 3^{4}$

Simplify the left side.

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

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

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

$v^{\frac{1}{4} \cdot 4} = 3^{4}$

Cancel the common factor of $4$ .

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Cancel the common factor.

$v^{\frac{1}{4} \cdot 4} = 3^{4}$

Rewrite the expression.

$v^{1} = 3^{4}$

Simplify.

$v = 3^{4}$

Simplify the right side.

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Raise $3$ to the power of $4$ .

$v = 81$