Question

How do you simplify `((3y^3)(2y^2)^-2)/(y^4)^3` and write it using only positive exponents?

Answer 1

`3/(4y^13`

Explanation:

You can get rid of the negative index by using one of the laws of indices: `x^-m = 1/x^m`
The whole bracket moves to the denominator and the index becomes positive.

`((3y^3)color(red)((2y^2)^-2))/(y^4)^3 = (3y^3)/(color(red)((2y^2)^2)(y^4)^3)`

Now use the power law of indices `(x^m)^n = x^mn`

`(3y^3)/((4y^4 y^12)`

Simplifying gives:

`3/(4y^13`