Provide two different ways to simplify each of the problems below. Please write all final answers using positive exponents.

Question

(-4m^-2 n^2)^3 * (2m^3 n)^-1

method 1: method 2:

(X^-1/2 Y^3)^-2
--------------------
XY^1/3 * X^2 Y^-4

Answer 1

(-4)^3 m^-6 n^6 2^-1 m^-3 n^-1
(-64) m^-9 n^5/2
-32 n^5/m^9

===========
(-4m^-2 n^2)^3 / (2m^3 n)
-1^3 * 2^6 * n^6 / [m^6 * n * 2 m^3]
-1 * 2^5 * n^5 /m^9
-32 n^5/m^9