Question

Simplify (xy)^-3/(x^-5y)^3

Answer 1

$Use:\\\\(a\cdot b)^n=a^n\cdot b^n\\\\a^n:a^m=a^{n-m}\\\\\left(a^n\right)^m=a^{n\cdot m}\\\\a^{-n}=\left(\frac{1}{a}\right)^{n}\\==================================\\\frac{(xy)^{-3}}{(x^{-5}y)^3}=\frac{x^{-3}y^{-3}}{(x^{-5})^3y^3}=\frac{x^{-3}y^{-3}}{x^{-15}y^3}=x^{-3-(-15)}y^{-3-3}=\boxed{x^{12}y^{-6}=\frac{x^{12}}{y^6}}$