How do you simplify these two radical expressions?

Question

(√(a^6)(b^3) - 4(a^5)(b^4) + 4(a^4)(b^5)) ----the entire expression is under a square root

(^3√20(x^2)(y)) (^3√16(x^2)(y^5)) -------those are cube roots in the index

Answer 1

Factor out the common values, which will be a^4b^3

√a^4b^3(a²-4ab+4b²) , anything squared can be moved outside the radical by square rooting it, such as a^4b^2, which will leave a b inside

a²b√b(a²-4ab+4b²) , factor the a²-4ab+4b² part now

a²b√b(a-2b)(a-2b), which is just a²b√b(a-2b)² , which we can remove from the radical

a²b(a-2b)√b