Answer
$xyz^2\sqrt[5] {(16y^4z)}$.
Work Step by Step
The given expression is
$=\sqrt[5] {2x^4y^3z^4}\cdot \sqrt[5] {8xy^6z^7}$
Use the product rule.
$=\sqrt[5] {2x^4y^3z^4\cdot 8xy^6z^7}$
Simplify.
$=\sqrt[5] {16x^5y^9z^{11}}$
Factor the terms.
$=\sqrt[5] {16x^5y^5y^4z^{10}z}$
Group the powers of $5$.
$=\sqrt[5] {(x^5y^5z^{10})(16y^4z)}$
Use the product rule
$=\sqrt[5] {(x^5y^5z^{10})}\sqrt[5] {(16y^4z)}$
Simplify.
$=xyz^2\sqrt[5] {(16y^4z)}$.
