Solve for a (x^(2/5))^6=x^a

${(x^{\frac{2}{5}})}^{6} = x^{a}$

Rewrite the equation as $x^{a} = {(x^{\frac{2}{5}})}^{6}$ .

$x^{a} = {(x^{\frac{2}{5}})}^{6}$

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

$x^{a} = x^{\frac{2}{5} \cdot 6}$

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

$a = \frac{2}{5} \cdot 6$

Multiply $\frac{2}{5} \cdot 6$ .

Combine $\frac{2}{5}$ and $6$ .

$a = \frac{2 \cdot 6}{5}$

Multiply $2$ by $6$ .

$a = \frac{12}{5}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{12}{5}$

Decimal Form:

$a = 2.4$

Mixed Number Form:

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