Simplify (x^(2/9))^(3/8)

${(x^{\frac{2}{9}})}^{\frac{3}{8}}$

Step 1

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

$x^{\frac{2}{9} \cdot \frac{3}{8}}$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

Step 5

Multiply $3$ by $4$ .

$x^{\frac{1}{12}}$