Solve by Factoring cube root of x-16=2

$\sqrt[3]{x - 16} = 2$

Step 1

Subtract $2$ from both sides of the equation.

$\sqrt[3]{x - 16} - 2 = 0$

Step 2

Add $2$ to both sides of the equation.

$\sqrt[3]{x - 16} = 2$

Step 3

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

${\sqrt[3]{x - 16}}^{3} = 2^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 16}$ as ${(x - 16)}^{\frac{1}{3}}$ .

${({(x - 16)}^{\frac{1}{3}})}^{3} = 2^{3}$

Simplify the left side.

Simplify ${({(x - 16)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(x - 16)}^{\frac{1}{3}})}^{3}$ .

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

${(x - 16)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x - 16)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

${(x - 16)}^{1} = 2^{3}$

Simplify.

$x - 16 = 2^{3}$

Simplify the right side.

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

$x - 16 = 8$

Step 5

Move all terms not containing $x$ to the right side of the equation.

Add $16$ to both sides of the equation.

$x = 8 + 16$

Add $8$ and $16$ .

$x = 24$