Answer
$(x-y)^2\sqrt[3] {(x-y)^{2}}$.
Work Step by Step
The given expression is
$=\sqrt[3] {x-y} \cdot \sqrt[3] {(x-y)^7}$
Apply product rule
$=\sqrt[n] a \cdot \sqrt[n] b = \sqrt[n] {ab}$
$=\sqrt[3] {(x-y) \cdot (x-y)^7}$
$=\sqrt[3] {(x-y)^1 \cdot (x-y)^7}$
Use $a^n\cdot a^m = a^{m+n}$
$=\sqrt[3] {(x-y)^{1+7}}$
$=\sqrt[3] {(x-y)^{8}}$
Further simplify by using product rule.
$=\sqrt[3] {(x-y)^{3+3+2}}$
$=\sqrt[3] {(x-y)^{3}(x-y)^{3}(x-y)^{2}}$
$=(x-y)(x-y)\sqrt[3] {(x-y)^{2}}$
$=(x-y)^2\sqrt[3] {(x-y)^{2}}$.
