Simplify (x^(5/8))^(2/3)

${(x^{\frac{5}{8}})}^{\frac{2}{3}}$

Step 1

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

$x^{\frac{5}{8} \cdot \frac{2}{3}}$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$x^{\frac{5}{2 (4)} \cdot \frac{2}{3}}$

Cancel the common factor.

$x^{\frac{5}{2 \cdot 4} \cdot \frac{2}{3}}$

Rewrite the expression.

$x^{\frac{5}{4} \cdot \frac{1}{3}}$

Step 3

Multiply $\frac{5}{4}$ by $\frac{1}{3}$ .

$x^{\frac{5}{4 \cdot 3}}$

Step 4

Multiply $4$ by $3$ .

$x^{\frac{5}{12}}$