Answer
$36x^4y^6\sqrt[5] {686x^2}$
Work Step by Step
First, we have to make sure that the indices are the same, which they are, in this exercise.
We now multiply the radicands and the coefficients:
$12x^2y • 3xy^3\sqrt[5] {7x^3y^4 • 98x^4y^6}$
Multiply the constants and add like variables:
$36x^3y^4\sqrt[5] {686x^7y^10}$
Rewrite the radicand as the product of two factors. One of the factors should be such that we can take its fifth root to remove it from under the radical sign:
$36x^3y^4\sqrt[5] {686 • x^5 • x^2 • y^{10}}$
Take the fifth roots of the factors in the radicand:
$36x^3y^4 • x • y^2\sqrt[5] {686x^2}$
Multiply coefficients together:
$36x^4y^6\sqrt[5] {686x^2}$