Question

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

Answer 1

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