Provide two different methods to simplify each of the problems below. Please write all final answers using positive exponents.
Q One:
(-4m^-2 n^2)^3 * (2m^3 n)^-1
Q Two:
(X^-1/2 Y^3)^-2
--------------------
XY^1/3 * X^2 Y^-4
method 1: multiply out all the exponents
method 2: convert to fraction with all positive exponents and cancel factors top and bottom
(-4m^-2 n^2)^3 * (2m^3 n)^-1
= -64m^-6n^6 * 1/2 m^-3 n^-1
= -32 m^-9 n^5
(-4m^-2 n^2)^3 * (2m^3 n)^-1
= -64n^6/m^6 * 1/(2m^3 n)
= -32n^5/m^9
work the other the same way