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

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

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

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

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

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

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

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

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

Multiply $\frac{6}{5}$ by $\frac{6}{5}$ .

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

Multiply $6$ by $6$ .

$a = \frac{36}{5 \cdot 5}$

Multiply $5$ by $5$ .

$a = \frac{36}{25}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{36}{25}$

Decimal Form:

$a = 1.44$

Mixed Number Form:

$a = 1 \frac{11}{25}$