Question

(2x^4y^-5)^3 (4x^-4y)^-2

Answer 1

`(2x^4y^(-5))^3 (4x^(-4)y)^(-2 )\ \ \ \boxed{\text{use}\ (ab)^n=a^nb^n}\\\\=[2^3(x^4)^3(y^(-5))^3]\cdot[4^(-2)(x^(-4))^(-2)y^(-2)]\ \ \ \boxed{\text{use}\ (a^n)^m=a^(nm)\ \text{and}\ a^(-n)=(1)/(a^n)}\\\\=(8x^(12)y^(-15))\left((1)/(4^2)x^(8)y^(-2)\right)=\left(8\cdot(1)/(16)\right)(x^(12)x^(8))(y^(-15)y^(-2))\\\boxed{\text{use}\ a^n\cdot a^m=a^(n+m)}\\\\=(1)/(2)x^(20)y^(-17)=(x^(20))/(2y^(17))`