Basic Math Examples

$\sqrt[3]{m^{2}} = 9$

Step 1

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

${\sqrt[3]{m^{2}}}^{3} = 9^{3}$

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

${(m^{\frac{2}{3}})}^{3} = 9^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

$m^{\frac{2}{3} \cdot 3} = 9^{3}$

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.

$m^{\frac{2}{3} \cdot 3} = 9^{3}$

Step 2.2.1.2.2

Rewrite the expression.

$m^{2} = 9^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $9$ to the power of $3$ .

$m^{2} = 729$

Step 3

Solve for $m$ .

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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.

$m = \pm \sqrt{729}$

Step 3.2

Simplify $\pm \sqrt{729}$ .

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Step 3.2.1

Rewrite $729$ as $27^{2}$ .

$m = \pm \sqrt{27^{2}}$

Step 3.2.2

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

$m = \pm 27$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.3.1

First, use the positive value of the $\pm$ to find the first solution.

$m = 27$

Step 3.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$m = - 27$

Step 3.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$m = 27, - 27$