Simplify ((x^2)/27)^(1/3)

${(\frac{x^{2}}{27})}^{\frac{1}{3}}$

Step 1

Apply basic rules of exponents.

Apply the product rule to $\frac{x^{2}}{27}$ .

$\frac{{(x^{2})}^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

Multiply the exponents in ${(x^{2})}^{\frac{1}{3}}$ .

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

$\frac{x^{2 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Combine $2$ and $\frac{1}{3}$ .

$\frac{x^{\frac{2}{3}}}{27^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x^{\frac{2}{3}}}{3^{1}}$

Evaluate the exponent.

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