Square root of X exponent 4 y over

Question

4 Square root of X exponent 2 y exponent 8

equals X exponent 2 over Y exponent 7
equals X -2X-1/3 (WHY?)
equals X3/2 square root of y/y exponent 2 (WHY?)

*I understand this is the answer, but when I look at what my teacher wrote, I do not understand the steps. Please help me with the steps!

Answer 1

√(x^4y) / 4√(x^2y^8)

Now, you know that √x^2 = x, so you have

(x^2 √y) / 4xy^4
= x√y / 4y^3

Apparently I have not parsed you English words correctly into algebra. Using my symbols (copy/paste), repost so the algebra is clear.

At any rate, just recall that

√x = x^(1/2)
√(x^n) = x^(n/2)

(x^a)^b = x^(ab)
x^a/x^b = x^(a-b)