Simplify the following:
(2 m^3 n^2)^4 (-m n^5)^2
Multiply each exponent in -m n^5 by 2:
(2 m^3 n^2)^4 (-1)^2 m^2 n^(2×5)
2×5 = 10:
(-1)^2 (2 m^3 n^2)^4 m^2 n^10
(-1)^2 = 1:
(2 m^3 n^2)^4 m^2 n^10
Multiply each exponent in 2 m^3 n^2 by 4:
2^4 m^(4×3) n^(4×2) m^2 n^10
4×2 = 8:
2^4 m^(4×3) n^8 m^2 n^10
4×3 = 12:
2^4 m^12 n^8 m^2 n^10
2^4 = (2^2)^2:
(2^2)^2 m^12 n^8 m^2 n^10
2^2 = 4:
4^2 m^12 n^8 m^2 n^10
4^2 = 16:
16 m^12 n^8 m^2 n^10
16 m^12 n^8 m^2 n^10 = 16 m^(12+2) n^(8+10):
16 m^(12+2) n^(8+10)
8+10 = 18:
16 m^(12+2) n^18
12+2 = 14:
Answer: | 16 m^14 n^18
