Question

Simplify with positive exponents... Show your work..

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

Answer 1

remember some basic rules

`(ab)^c=(a^c)(b^c)` and

`(a^b)^c=a^(bc)` and

`x^(-m)= (1)/(x^m)`
so


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

`(3x^(-2))^4=(3^4)((x^(-2)^4)=(81)(x^(-8))`

`(y^5)^4=y^(20)`
we now have

`81x^(-8)y^(20)`

`x^(-8)= (1)/(x^8)` so

`81x^(-8)y^(20)= (81y^(20))/(x^8)`

Answer 2

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

= 81x^-8 y^20

=81y^20
------------
x^8