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

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

Step 1

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

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

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

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

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

Step 2

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

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

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

Multiply $2 (\frac{2}{3})$ .

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

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

Multiply $2$ by $2$ .

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

Step 3

Move $x^{\frac{2}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{1}{x^{\frac{4}{3}} x^{- \frac{2}{3}}}$

Step 4

Multiply $x^{\frac{4}{3}}$ by $x^{- \frac{2}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{x^{\frac{4}{3} - \frac{2}{3}}}$

Combine the numerators over the common denominator.

$\frac{1}{x^{\frac{4 - 2}{3}}}$

Subtract $2$ from $4$ .

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