Algebra Examples

$\sqrt[3]{x^{5}} = 32$

Step 1

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

${\sqrt[3]{x^{5}}}^{3} = 32^{3}$

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 $\sqrt[3]{x^{5}}$ as $x^{\frac{5}{3}}$ .

${(x^{\frac{5}{3}})}^{3} = 32^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply the exponents in ${(x^{\frac{5}{3}})}^{3}$ .

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Step 2.2.1.1

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

$x^{\frac{5}{3} \cdot 3} = 32^{3}$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Cancel the common factor.

$x^{\frac{5}{3} \cdot 3} = 32^{3}$

Step 2.2.1.2.2

Rewrite the expression.

$x^{5} = 32^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $32$ to the power of $3$ .

$x^{5} = 32768$

Step 3

Solve for $x$ .

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Step 3.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[5]{32768}$

Step 3.2

Simplify $\sqrt[5]{32768}$ .

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Step 3.2.1

Rewrite $32768$ as $8^{5}$ .

$x = \sqrt[5]{8^{5}}$

Step 3.2.2

Pull terms out from under the radical, assuming real numbers.

$x = 8$