Solve for a (x^(2/3))^(5/6)=x^a

${(x^{\frac{2}{3}})}^{\frac{5}{6}} = x^{a}$

Rewrite the equation as $x^{a} = {(x^{\frac{2}{3}})}^{\frac{5}{6}}$ .

$x^{a} = {(x^{\frac{2}{3}})}^{\frac{5}{6}}$

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

$x^{a} = x^{\frac{2}{3} \cdot \frac{5}{6}}$

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

$a = \frac{2}{3} \cdot \frac{5}{6}$

Simplify $\frac{2}{3} \cdot \frac{5}{6}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $3$ by $3$ .

$a = \frac{5}{9}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{5}{9}$

Decimal Form:

$a = 0.\overline{5}$