You want to factor the expression under the radical (called the "radicand") and look for squared terms. For the first problem, the radicand is 27x3y6. Factoring:
27 = 9*3 = 32*3
x3 = x2*x
y6 = (y3)2
The squared terms are highlighted in orange. Hence:
3√27x3y6 = 3√{32*3*x2*x*(y3)2}
= 3√32√3√x2√x√(y3)2
= 3*3√3 * x√x * y3
= 9xy3√3x
Try the other three problems on your own in order to learn how to do it for yourself.
