Solve by Factoring cube root of 52x=-4

$\sqrt[3]{52 x} = - 4$

Step 1

Add $4$ to both sides of the equation.

$\sqrt[3]{52 x} + 4 = 0$

Step 2

Subtract $4$ from both sides of the equation.

$\sqrt[3]{52 x} = - 4$

Step 3

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

${\sqrt[3]{52 x}}^{3} = {(- 4)}^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{52 x}$ as ${(52 x)}^{\frac{1}{3}}$ .

${({(52 x)}^{\frac{1}{3}})}^{3} = {(- 4)}^{3}$

Simplify the left side.

Simplify ${({(52 x)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(52 x)}^{\frac{1}{3}})}^{3}$ .

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

${(52 x)}^{\frac{1}{3} \cdot 3} = {(- 4)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(52 x)}^{\frac{1}{3} \cdot 3} = {(- 4)}^{3}$

Rewrite the expression.

${(52 x)}^{1} = {(- 4)}^{3}$

Simplify.

$52 x = {(- 4)}^{3}$

Simplify the right side.

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

$52 x = - 64$

Step 5

Divide each term in $52 x = - 64$ by $52$ and simplify.

Divide each term in $52 x = - 64$ by $52$ .

$\frac{52 x}{52} = \frac{- 64}{52}$

Simplify the left side.

Cancel the common factor of $52$ .

Cancel the common factor.

$\frac{52 x}{52} = \frac{- 64}{52}$

Divide $x$ by $1$ .

$x = \frac{- 64}{52}$

Simplify the right side.

Cancel the common factor of $- 64$ and $52$ .

Factor $4$ out of $- 64$ .

$x = \frac{4 (- 16)}{52}$

Cancel the common factors.

Factor $4$ out of $52$ .

$x = \frac{4 \cdot - 16}{4 \cdot 13}$

Cancel the common factor.

$x = \frac{4 \cdot - 16}{4 \cdot 13}$

Rewrite the expression.

$x = \frac{- 16}{13}$

Move the negative in front of the fraction.

$x = - \frac{16}{13}$

Solve by Factoring cube root of 52x=-4

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