Simplify (8x^3)^(2/3)

${(8 x^{3})}^{\frac{2}{3}}$

Step 1

Simplify the expression.

Apply the product rule to $8 x^{3}$ .

$8^{\frac{2}{3}} {(x^{3})}^{\frac{2}{3}}$

Rewrite $8$ as $2^{3}$ .

${(2^{3})}^{\frac{2}{3}} {(x^{3})}^{\frac{2}{3}}$

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

$2^{3 (\frac{2}{3})} {(x^{3})}^{\frac{2}{3}}$

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

$2^{3 (\frac{2}{3})} {(x^{3})}^{\frac{2}{3}}$

Rewrite the expression.

$2^{2} {(x^{3})}^{\frac{2}{3}}$

Step 3

Simplify the expression.

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

$4 {(x^{3})}^{\frac{2}{3}}$

Multiply the exponents in ${(x^{3})}^{\frac{2}{3}}$ .

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

$4 x^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$4 x^{3 (\frac{2}{3})}$

Rewrite the expression.

$4 x^{2}$