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

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

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

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

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

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

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

One to any power is one.

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

Simplify the denominator.

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

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

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

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

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

Multiply $\frac{2}{3} \cdot 2$ .

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

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

Multiply $2$ by $2$ .

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