Answer
$-3\sqrt [3] {7xy} + 3\sqrt[5] {7xy}$
Work Step by Step
Rewrite each radicand as the product of two factors such that you can take the 3rd root or the 5th root of one of the factors, depending on the index:
$\sqrt [3] {7xy} + \sqrt[5] {7xy} - \sqrt [3] {4^3 • 7 • x • y} + \sqrt [5] {2^4 • 7 • xy}$
Take the 3rd or 4th roots of terms, depending on the index, to take them out from under the radical sign:
$\sqrt [3] {7xy} + \sqrt[5] {7xy} - 4\sqrt [3] {7xy} + 2\sqrt [5] {7xy}$
Combine like terms. Remember that like terms are those that have the same radical and the same index:
$-3\sqrt [3] {7xy} + 3\sqrt[5] {7xy}$
