Solve for a (x^(2/3))^(1/5)=x^a

${(x^{\frac{2}{3}})}^{\frac{1}{5}} = x^{a}$

Rewrite the equation as $x^{a} = {(x^{\frac{2}{3}})}^{\frac{1}{5}}$ .

$x^{a} = {(x^{\frac{2}{3}})}^{\frac{1}{5}}$

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

$x^{a} = x^{\frac{2}{3} \cdot \frac{1}{5}}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$a = \frac{2}{3} \cdot \frac{1}{5}$

Multiply $\frac{2}{3} \cdot \frac{1}{5}$ .

Multiply $\frac{2}{3}$ by $\frac{1}{5}$ .

$a = \frac{2}{3 \cdot 5}$

Multiply $3$ by $5$ .

$a = \frac{2}{15}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{2}{15}$

Decimal Form:

$a = 0.1\overline{3}$