Answer
The answer is $a^{\frac{1}{6}}$
Work Step by Step
To solve this
$a^{\frac{2}{3}}$$\times$$a^{x}$ = $a^{\frac{5}{6}}$
$a^{x}$ = $\frac{a^{\frac{5}{6}}}{a^{\frac{2}{3}}}$
$a^{x}$ = $a^{\frac{5}{6}-\frac{2}{3}}$
$a^{x}$ = $a^{\frac{5}{6}-\frac{4}{6}}$
$a^{x}$ = $a^{\frac{1}{6}}$ --> since bases are equal, make the exponents equal
x = $\frac{1}{6}$
Therefore the missing part is $a^{\frac{1}{6}}$.
