Answer:
(27 y^(-8))/(4 x^6)
Explanation:
Simplify the following:
(4 (3 x^2 y^4)^3)/(2 x^3 y^5)^4
Multiply each exponent in 2 x^3 y^5 by 4:
(4 (3 x^2 y^4)^3)/(2^4 x^(4×3) y^(4×5))
4×5 = 20:
(4 (3 x^2 y^4)^3)/(2^4 x^(4×3) y^20)
4×3 = 12:
(4 (3 x^2 y^4)^3)/(2^4 x^12 y^20)
2^4 = (2^2)^2:
(4 (3 x^2 y^4)^3)/((2^2)^2 x^12 y^20)
2^2 = 4:
(4 (3 x^2 y^4)^3)/(4^2 x^12 y^20)
4^2 = 16:
(4 (3 x^2 y^4)^3)/(16 x^12 y^20)
Multiply each exponent in 3 x^2 y^4 by 3:
(4×3^3 x^(3×2) y^(3×4))/(16 x^12 y^20)
3×4 = 12:
(4×3^3 x^(3×2) y^12)/(16 x^12 y^20)
3×2 = 6:
(4×3^3 x^6 y^12)/(16 x^12 y^20)
3^3 = 3×3^2:
(4×3×3^2 x^6 y^12)/(16 x^12 y^20)
3^2 = 9:
(4×3×9 x^6 y^12)/(16 x^12 y^20)
3×9 = 27:
(4×27 x^6 y^12)/(16 x^12 y^20)
4/16 = 4/(4×4) = 1/4:
(27 x^6 y^12)/(4 x^12 y^20)
Combine powers. (27 x^6 y^12)/(4 x^12 y^20) = (27 x^(6 - 12) y^(12 - 20))/4:
(27 x^(6 - 12) y^(12 - 20))/4
6 - 12 = -6:
(27 x^(-6) y^(12 - 20))/4
12 - 20 = -8:
Answer: (27 y^(-8))/(4 x^6)