Simplify 2( cube root of 12-5x)^3+8

$2 {(\sqrt[3]{12 - 5 x})}^{3} + 8$

Step 1

Simplify each term.

Rewrite ${\sqrt[3]{12 - 5 x}}^{3}$ as $12 - 5 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{12 - 5 x}$ as ${(12 - 5 x)}^{\frac{1}{3}}$ .

$2 {({(12 - 5 x)}^{\frac{1}{3}})}^{3} + 8$

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

$2 {(12 - 5 x)}^{\frac{1}{3} \cdot 3} + 8$

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

$2 {(12 - 5 x)}^{\frac{3}{3}} + 8$

Cancel the common factor of $3$ .

Cancel the common factor.

$2 {(12 - 5 x)}^{\frac{3}{3}} + 8$

Rewrite the expression.

$2 {(12 - 5 x)}^{1} + 8$

Simplify.

$2 (12 - 5 x) + 8$

Apply the distributive property.

$2 \cdot 12 + 2 (- 5 x) + 8$

Multiply $2$ by $12$ .

$24 + 2 (- 5 x) + 8$

Multiply $- 5$ by $2$ .

$24 - 10 x + 8$

Step 2

Add $24$ and $8$ .

$- 10 x + 32$