Answer
$3ab\sqrt [3] {2b}$
Work Step by Step
First, we have to make sure that the indices are the same, which they are, in this exercise.
Take the cube roots of perfect cubes in the radicand:
$a\sqrt [3] {3b^2} • \sqrt [3] {18b^2}$
We now multiply the coefficients and the radicands:
$a • 1\sqrt [3] {3b^2 • 18b^2}$
Perform the multiplication:
$a\sqrt [3] {54b^4}$
Rewrite the radicand so that we separate perfect cubes from other factors:
$a\sqrt [3] {3^3 • 2 • b^3 • b}$
Take the cube roots of the factors in the radicand:
$a • 3 • b\sqrt [3] {2b}$
Multiply coefficients together:
$3ab\sqrt [3] {2b}$
