Simplify:
(4mn^-2) ^3 * (2m)^2
A. 48m^5/ n^6
B. 256m^3 n
C. 48m^3 n
D. 256m^5/ n^6
To simplify the expression (4mn^-2)^3 * (2m)^2, we can simplify each part separately and then combine them.
First, let's simplify (4mn^-2)^3:
(4mn^-2)^3 = 4^3 * m^3 * n^(-2 * 3) = 64m^3 * n^(-6) = 64m^3 / n^6
Next, let's simplify (2m)^2:
(2m)^2 = 2^2 * m^2 = 4m^2
Now, let's combine the simplified parts:
(4mn^-2)^3 * (2m)^2 = (64m^3 / n^6) * 4m^2 = (64m^3 * 4m^2) / n^6 = 256m^5 / n^6
Therefore, the simplified expression is 256m^5 / n^6. The answer is option D.