Precalculus Examples

$v^{\frac{1}{4}} = 2$

Step 1

Raise each side of the equation to the power of $4$ to eliminate the fractional exponent on the left side.

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

Step 2

Simplify the exponent.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

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

Step 2.1.1.1.2

Cancel the common factor of $4$ .

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Step 2.1.1.1.2.1

Cancel the common factor.

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

Step 2.1.1.1.2.2

Rewrite the expression.

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

Step 2.1.1.2

Simplify.

$v = 2^{4}$

Step 2.2

Simplify the right side.

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Step 2.2.1

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

$v = 16$