Question

Simplify: (x4y5) ÷ (xy2)2.

A. x3y
B. x2y
C. x2
D. x3

Answer 1

When you have something that is basically a power raised to another power, like you have with (xy^2)^2, you can distribute that outside power inside of the parenthesis and multiply powers. So I can rewrite the (xy^2)^2 portion as:

\[(xy^{2})^{2} = x^{1*2}y^{2*2}= x^{2}y^{4}\] So given that I can rewrite it like that, I now have:

\[\frac{ x^{4}y^{5} }{ x^{2}y^{4} }\]

So now you have 2 x's on bottom that can cancel out 2 x's on top, leaving 2 x's total on top. And you have 4 y's on bottom that can cance; out 4 y's on top, leaving one left. SO 2 x' left and 1 y left, meanign your answer is

x^2y

Answer 2

thank you soooooo much @Psymon !!! ;D

Answer 3

of course : )