Pre-Algebra Examples

$\sqrt[3]{6 x} = - 5$

Step 1

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

${\sqrt[3]{6 x}}^{3} = {(- 5)}^{3}$

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 $\sqrt[3]{6 x}$ as ${(6 x)}^{\frac{1}{3}}$ .

${({(6 x)}^{\frac{1}{3}})}^{3} = {(- 5)}^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(6 x)}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(6 x)}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1.1

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

${(6 x)}^{\frac{1}{3} \cdot 3} = {(- 5)}^{3}$

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.

${(6 x)}^{\frac{1}{3} \cdot 3} = {(- 5)}^{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(6 x)}^{1} = {(- 5)}^{3}$

Step 2.2.1.2

Simplify.

$6 x = {(- 5)}^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $- 5$ to the power of $3$ .

$6 x = - 125$

Step 3

Divide each term in $6 x = - 125$ by $6$ and simplify.

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Step 3.1

Divide each term in $6 x = - 125$ by $6$ .

$\frac{6 x}{6} = \frac{- 125}{6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 125}{6}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 125}{6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x = - \frac{125}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{125}{6}$

Decimal Form:

$x = - 20.8\overline{3}$

Mixed Number Form:

$x = - 20 \frac{5}{6}$