Answer
$\sqrt[3] {a^2+ab+b^2}$.
Work Step by Step
The given expression is
$\frac{\sqrt[3] {a^3-b^3}}{\sqrt[3] {a-b}}$
Use the quotient rule $\frac{\sqrt[n] a}{\sqrt[n] b} = \sqrt[n] {\frac{a}{b}}$.
$=\sqrt[3] {\frac{a^3-b^3}{a-b}}$
Factor the numerator using the formula
$a^3-b^3=(a-b)(a^2+ab+b^2)$.
$=\sqrt[3] {\frac{(a-b)(a^2+ab+b^2)}{a-b}}$
Cancel out common terms.
$=\sqrt[3] {a^2+ab+b^2}$.
