Solve for x cube root of 24x=-3

$\sqrt[3]{24 x} = - 3$

Step 1

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

${\sqrt[3]{24 x}}^{3} = {(- 3)}^{3}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{24 x}$ as ${(24 x)}^{\frac{1}{3}}$ .

${({(24 x)}^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Simplify the left side.

Simplify ${({(24 x)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(24 x)}^{\frac{1}{3}})}^{3}$ .

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

${(24 x)}^{\frac{1}{3} \cdot 3} = {(- 3)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(24 x)}^{\frac{1}{3} \cdot 3} = {(- 3)}^{3}$

Rewrite the expression.

${(24 x)}^{1} = {(- 3)}^{3}$

Simplify.

$24 x = {(- 3)}^{3}$

Simplify the right side.

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

$24 x = - 27$

Step 3

Divide each term in $24 x = - 27$ by $24$ and simplify.

Divide each term in $24 x = - 27$ by $24$ .

$\frac{24 x}{24} = \frac{- 27}{24}$

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24 x}{24} = \frac{- 27}{24}$

Divide $x$ by $1$ .

$x = \frac{- 27}{24}$

Simplify the right side.

Cancel the common factor of $- 27$ and $24$ .

Factor $3$ out of $- 27$ .

$x = \frac{3 (- 9)}{24}$

Cancel the common factors.

Factor $3$ out of $24$ .

$x = \frac{3 \cdot - 9}{3 \cdot 8}$

Cancel the common factor.

$x = \frac{3 \cdot - 9}{3 \cdot 8}$

Rewrite the expression.

$x = \frac{- 9}{8}$

Move the negative in front of the fraction.

$x = - \frac{9}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{9}{8}$

Decimal Form:

$x = - 1.125$

Mixed Number Form:

$x = - 1 \frac{1}{8}$

Solve for x cube root of 24x=-3

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