Algebra Examples

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

To remove the radical on the left side of the equation, cube both sides of the equation.

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

Simplify each side of the equation.

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{u}$ as $u^{\frac{1}{3}}$ .

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

Simplify the left side.

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Simplify ${(u^{\frac{1}{3}})}^{3}$ .

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Multiply the exponents in ${(u^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$u = 4^{3}$

Simplify the right side.

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

$u = 64$