Simplify the following:((4 g^3 h^2 k^4)^3 g^3 h^2)/8 - (h^5 k^3)^5
Multiply each exponent in 4 g^3 h^2 k^4 by 3:(4^3 g^(3×3) h^(3×2) k^(3×4) g^3 h^2)/8 - (h^5 k^3)^5
3×3 = 9:(4^3 g^9 h^(3×2) k^(3×4) g^3 h^2)/8 - (h^5 k^3)^5
3×2 = 6:(4^3 g^9 h^6 k^(3×4) g^3 h^2)/8 - (h^5 k^3)^5
3×4 = 12:(4^3 g^9 h^6 k^12 g^3 h^2)/8 - (h^5 k^3)^5
Combine powers. (4^3 g^9 h^6 k^12 g^3 h^2)/8 = (4^3 g^(9 + 3) h^(6 + 2) k^12)/8:(4^3 g^(9 + 3) h^(6 + 2) k^12)/8 - (h^5 k^3)^5
9 + 3 = 12:(4^3 g^12 h^(6 + 2) k^12)/8 - (h^5 k^3)^5
6 + 2 = 8:(4^3 g^12 h^8 k^12)/8 - (h^5 k^3)^5
4^3 = 4×4^2:(4×4^2 g^12 h^8 k^12)/8 - (h^5 k^3)^5
4^2 = 16:(4×16 g^12 h^8 k^12)/8 - (h^5 k^3)^5
4×16 = 64:(64 g^12 h^8 k^12)/8 - (h^5 k^3)^5
64/8 = (8×8)/8 = 8:8 g^12 h^8 k^12 - (h^5 k^3)^5
Multiply each exponent in h^5 k^3 by 5:8 g^12 h^8 k^12 - h^(5×5) k^(5×3)
5×3 = 15:8 g^12 h^8 k^12 - h^(5×5) k^15
5×5 = 25:8 g^12 h^8 k^12 - h^25 k^15
Factor h^8 k^12 out of 8 g^12 h^8 k^12 - h^25 k^15:Answer: h^8 k^12 (8 g^12 - h^17 k^3)
