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

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

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

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

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

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

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

$a = 2 (\frac{2}{3})$

Multiply $2 (\frac{2}{3})$ .

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

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

Multiply $2$ by $2$ .

$a = \frac{4}{3}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{4}{3}$

Decimal Form:

$a = 1.\overline{3}$

Mixed Number Form:

$a = 1 \frac{1}{3}$