Simplify ( cube root of 2x-15)^3-6

${(\sqrt[3]{2 x - 15})}^{3} - 6$

Step 1

Rewrite ${\sqrt[3]{2 x - 15}}^{3}$ as $2 x - 15$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x - 15}$ as ${(2 x - 15)}^{\frac{1}{3}}$ .

${({(2 x - 15)}^{\frac{1}{3}})}^{3} - 6$

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

${(2 x - 15)}^{\frac{1}{3} \cdot 3} - 6$

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

${(2 x - 15)}^{\frac{3}{3}} - 6$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 x - 15)}^{\frac{3}{3}} - 6$

Rewrite the expression.

${(2 x - 15)}^{1} - 6$

Simplify.

$2 x - 15 - 6$

Step 2

Subtract $6$ from $- 15$ .

$2 x - 21$