Answer
$40a^4b^2\sqrt [4] {2ab^3}$.
Work Step by Step
The given expression is
$=(5a^2b\sqrt [4] {8a^2b})(4ab\sqrt [4]{4a^3b^2})$
Clear the parentheses.
$=20a^3b^2\sqrt [4] {8a^2b}\sqrt [4] {4a^3b^2}$
Apply the product rule of radicals.
$\sqrt [4]a \cdot \sqrt [4] b = \sqrt [4] {ab}$
$=20a^3b^2\sqrt [4] {8a^2b\cdot 4a^3b^2}$
Find the factors:
$=20a^3b^2\sqrt [4] {2^42a^4ab^3}$
Factor into two radicals.
$=20a^3b^2\sqrt [4] {2^4a^4}\sqrt [4] {2ab^3}$
Simplify.
$=20a^3b^2\cdot 2a\sqrt [4] {2ab^3}$
$=40a^4b^2\sqrt [4] {2ab^3}$.
