Simplify ( cube root of x-9)^3

${(\sqrt[3]{x - 9})}^{3}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 9}$ as ${(x - 9)}^{\frac{1}{3}}$ .

${({(x - 9)}^{\frac{1}{3}})}^{3}$

Step 2

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

${(x - 9)}^{\frac{1}{3} \cdot 3}$

Step 3

Combine $\frac{1}{3}$ and $3$ .

${(x - 9)}^{\frac{3}{3}}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

${(x - 9)}^{\frac{3}{3}}$

Rewrite the expression.

${(x - 9)}^{1}$

Step 5

Simplify.

$x - 9$