Question

How to simplify `(-3x^-2y)^-1` in the positive exponential notation?

Answer 1

See a solution process below:

Explanation:

We can eliminate the outer exponent using these rules of exponents:

`x^color(red)(a) = 1/x^color(red)(-a)` and `a^color(red)(1) = a`

`(-3x^-2y)^color(red)(-1) => 1/(-3x^-2y)^color(red)(- -1) => 1/(-3x^-2y)^color(red)(1) =>`

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

Next, use this rule of exponents on the `x` term to eliminate the final negative exponent:

`1/x^color(red)(a) = x^color(red)(-a)`

`1/(-3x^color(red)(-2)y) => x^color(red)(- -2)/(-3y) => x^2/(-3y) => -x^2/(3y)`