Question

How to simplify `((3x^-1)/(9y^2))^-2` and have the answer in positive exponential notation?

Answer 1

`((3x^-1)/(9y^2))^-2=9x^2y^4`

Explanation:

You will need the following index laws

(1) `(x/y)^a=x^a/y^a`

(2) `(kx^a)^b=k^bx^(ab)`

(3) `x^-a=1/x^a`

(4) `1/x^-a=x^a`

First apply (1)

`((3x^-1)/(9y^2))^-2=(3x^-1)^-2/(9y^2)^-2`

Then apply (2)

`(3x^-1)^-2/(9y^2)^-2=(3^-2x^2)/(9^-2y^-4)`

Finally, apply (3) and (4)

`(3^-2x^2)/(9^-2y^-4)=(9^2x^2y^4)/3^2=9x^2y^4`