Answer
$(x-6)^2\sqrt[3] {(x-6)^{2}}$.
Work Step by Step
The given expression is
$=\sqrt[3] {x-6} \cdot \sqrt[3] {(x-6)^7}$
Apply product rule
$=\sqrt[n] a \cdot \sqrt[n] b = \sqrt[n] {ab}$
$=\sqrt[3] {(x-6) \cdot (x-6)^7}$
$=\sqrt[3] {(x-6)^1 \cdot (x-6)^7}$
Use $a^n\cdot a^m = a^{m+n}$
$=\sqrt[3] {(x-6)^{1+7}}$
$=\sqrt[3] {(x-6)^{8}}$
Further simplify by using product rule.
$=\sqrt[3] {(x-6)^{3+3+2}}$
$=\sqrt[3] {(x-6)^{3}(x-6)^{3}(x-6)^{2}}$
$=(x-6)(x-6)\sqrt[3] {(x-6)^{2}}$
$=(x-6)^2\sqrt[3] {(x-6)^{2}}$.
