Simplify :

$a^{\dfrac{4}{3}} ÷ a^{\dfrac{-2}{3}}$

Given,

$a^{\dfrac{4}{3}} ÷ a^{\dfrac{-2}{3}}$

Simplifying the expression :

$\Rightarrow a^{\dfrac{4}{3}} ÷ a^{\dfrac{-2}{3}} \\[1em] \Rightarrow \dfrac{a^{\dfrac{4}{3}}}{a^{\dfrac{-2}{3}}} \\[1em] \Rightarrow a^{\dfrac{4}{3} - \Big(-\dfrac{2}{3}\Big)} \\[1em] \Rightarrow a^{\dfrac{4 - (-2)}{3}} \\[1em] \Rightarrow a^{\dfrac{4 + 2}{3}} \\[1em] \Rightarrow a^{\dfrac{6}{3}} \\[1em] \Rightarrow a^2.$

Hence, $a^{\dfrac{4}{3}} ÷ a^{\dfrac{-2}{3}}= a^2$.