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

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Combine.

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

Step 3

Multiply $2$ by $1$ .

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

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2}{3 x^{\frac{1}{3}}}$ .

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

Apply the product rule to $3 x^{\frac{1}{3}}$ .

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

Step 5

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

$\frac{4}{3^{2} {(x^{\frac{1}{3}})}^{2}}$

Step 6

Simplify the denominator.

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

$\frac{4}{9 {(x^{\frac{1}{3}})}^{2}}$

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

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

$\frac{4}{9 x^{\frac{1}{3} \cdot 2}}$

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

$\frac{4}{9 x^{\frac{2}{3}}}$