Answer
$\frac{\sqrt [3] {18b^2}}{3}$
Work Step by Step
We don't want to leave radicals in the denominator, so to get rid of radicals in the denominator, we multiply both the numerator and denominator by as many factors that are needed to eliminate the radical. In this case, we need to multiply the denominator by two more 6's and two more a's to eliminate the radical. We multiply the numerator by the same factor:
$\frac{\sqrt [3] {4ab^2}}{\sqrt [3] {6a}} • \frac{\sqrt [3] {6^2a^2}}{\sqrt [3] {6^2a^2}}$
Multiply to simplify:
$\frac{\sqrt [3] {144a^3b^2}}{\sqrt [3] {6^3a^3}}$
Rewrite radicands as the product of two factors. One of the factors should be a perfect cube so we can take its cube root to remove it from under the radical sign:
$\frac{\sqrt [3] {2^3 • 18 • a^3 • b^2}}{\sqrt [3] {6^3a^3}}$
Take the cube root of any perfect cubes:
$\frac{2a\sqrt [3] {18b^2}}{6a}$
Cancel any factors common in both numerator and denominator:
$\frac{\sqrt [3] {18b^2}}{3}$
