Answer
$(x-2)\sqrt[7] {(x-2)^{2} }$.
Work Step by Step
The given expression is
$=\sqrt[7] {(x-2)^3}\cdot \sqrt[7] {(x-2)^6}$
Use the product rule.
$=\sqrt[7] {(x-2)^3\cdot(x-2)^6 }$
Use power rule.
$=\sqrt[7] {(x-2)^{3+6} }$
Simplify.
$=\sqrt[7] {(x-2)^{9} }$
Factor as a power of $7$.
$=\sqrt[7] {(x-2)^{7+2} }$
Use power rule.
$=\sqrt[7] {(x-2)^{7}(x-2)^{2} }$
Simplify.
$=(x-2)\sqrt[7] {(x-2)^{2} }$.
