Simplify (64/x)^(2/3)

${(\frac{64}{x})}^{\frac{2}{3}}$

Step 1

Apply the product rule to $\frac{64}{x}$ .

$\frac{64^{\frac{2}{3}}}{x^{\frac{2}{3}}}$

Step 2

Simplify the numerator.

Rewrite $64$ as $4^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Raise $4$ to the power of $2$ .

$\frac{16}{x^{\frac{2}{3}}}$