Simplify (27x^3)^(2/3)

${(27 x^{3})}^{\frac{2}{3}}$

Step 1

Simplify the expression.

Apply the product rule to $27 x^{3}$ .

$27^{\frac{2}{3}} {(x^{3})}^{\frac{2}{3}}$

Rewrite $27$ as $3^{3}$ .

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

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

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

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify the expression.

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

$9 {(x^{3})}^{\frac{2}{3}}$

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

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

$9 x^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$9 x^{3 (\frac{2}{3})}$

Rewrite the expression.

$9 x^{2}$