Algebra Examples

$\sqrt[3]{2 m} = 4$

Step 1

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

${\sqrt[3]{2 m}}^{3} = 4^{3}$

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 $\sqrt[3]{2 m}$ as ${(2 m)}^{\frac{1}{3}}$ .

${({(2 m)}^{\frac{1}{3}})}^{3} = 4^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(2 m)}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(2 m)}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1.1

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

${(2 m)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(2 m)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(2 m)}^{1} = 4^{3}$

Step 2.2.1.2

Simplify.

$2 m = 4^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$2 m = 64$

Step 3

Divide each term in $2 m = 64$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 m = 64$ by $2$ .

$\frac{2 m}{2} = \frac{64}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 m}{2} = \frac{64}{2}$

Step 3.2.1.2

Divide $m$ by $1$ .

$m = \frac{64}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $64$ by $2$ .

$m = 32$