Which expression is equivalent to [(3xy^-5)^3/(x^-2y^2)^-4]^-2?a. x^10y^14/729b. x^22/18y^46c. 729/x^10y^14d. 18y^46/x^22
Accepted Solution
A:
Answer:- a.The given expression is equivalent to [tex]\frac{x^{10}y^{14}}{729}[/tex]
Given expression:- [tex][\frac{(3xy^{-5})^3}{(x^{-2}y^2)^{-4}}]^{-2}[/tex][tex]=[\frac{(3)^3x^3y^{-5\times3}}{x^{-2\times-4}y^{2\times-4}}]^{-2}.........(a^m)^n=a^{mn}[/tex][tex]=[\frac{27x^3y^{-15}}{x^8y^{-8}}]^{-2}[/tex][tex]=[27x^{3-8}y^{-15-(-8)}]^{-2}............\frac{a^m}{a^n}=a^{m-n}[/tex][tex]=[27x^{-5}y^{-7}]^{-2}=(27)^{-2}(x^{-5})^{-2}(y^{-7})^{-2}.........(a^m)^n=a^{mn}[/tex][tex]=\frac{1}{(27)^2}(x^{10}y^{14})=\frac{x^{10}y^{14}}{729}[/tex]Thus a. is the right answer.