Question

Which expression is equivalent to [(3xy^-5)^3/(x^-2y^2)^-4]^-2?

a. x^10y^14/729
b. x^22/18y^46
c. 729/x^10y^14
d. 18y^46/x^22

Answer 1

Answer: A

Explanation:

built different

Answer 2

Answer:- a.The given expression is equivalent to
`(x^(10)y^(14))/(729)`

Given expression:-
`[((3xy^(-5))^3)/((x^(-2)y^2)^(-4))]^(-2)`

`=[((3)^3x^3y^(-5*3))/(x^(-2*-4)y^(2*-4))]^(-2).........(a^m)^n=a^(mn)`

`=[(27x^3y^(-15))/(x^8y^(-8))]^(-2)`

`=[27x^(3-8)y^(-15-(-8))]^(-2)............(a^m)/(a^n)=a^(m-n)`

`=[27x^(-5)y^(-7)]^(-2)=(27)^(-2)(x^(-5))^(-2)(y^(-7))^(-2).........(a^m)^n=a^(mn)`

`=(1)/((27)^2)(x^(10)y^(14))=(x^(10)y^(14))/(729)`

Thus a. is the right answer.