Solve by Factoring cube root of 24x=-3

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

Step 1

Add $3$ to both sides of the equation.

$\sqrt[3]{24 x} + 3 = 0$

Step 2

Simplify each term.

Rewrite $24 x$ as $2^{3} \cdot (3 x)$ .

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3) x} + 3 = 0$

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} \cdot 3 x} + 3 = 0$

Add parentheses.

$\sqrt[3]{2^{3} \cdot (3 x)} + 3 = 0$

Pull terms out from under the radical.

$2 \sqrt[3]{3 x} + 3 = 0$

Step 3

Subtract $3$ from both sides of the equation.

$2 \sqrt[3]{3 x} = - 3$

Step 4

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

${(2 \sqrt[3]{3 x})}^{3} = {(- 3)}^{3}$

Step 5

Simplify each side of the equation.

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

${(2 {(3 x)}^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Simplify the left side.

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

Apply the product rule to $3 x$ .

${(2 (3^{\frac{1}{3}} x^{\frac{1}{3}}))}^{3} = {(- 3)}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 \cdot 3^{\frac{1}{3}} x^{\frac{1}{3}}$ .

${(2 \cdot 3^{\frac{1}{3}})}^{3} {(x^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Apply the product rule to $2 \cdot 3^{\frac{1}{3}}$ .

$2^{3} \cdot {(3^{\frac{1}{3}})}^{3} {(x^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Raise $2$ to the power of $3$ .

$8 \cdot {(3^{\frac{1}{3}})}^{3} {(x^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

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

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

$8 \cdot 3^{\frac{1}{3} \cdot 3} {(x^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$8 \cdot 3^{\frac{1}{3} \cdot 3} {(x^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Rewrite the expression.

$8 \cdot 3^{1} {(x^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Evaluate the exponent.

$8 \cdot 3 {(x^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Multiply $8$ by $3$ .

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

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

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 6

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.

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

Solve by Factoring cube root of 24x=-3

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