Question

Question #fb92a

Answer 1

If the question is to simplify this expression and ensure there are no negative exponents then see the solution process below:

`(-25m^5n^-5)/(5m^-4n^-2)`

Explanation:

First, we can simplify the constants:

`(color(red)(-25)m^5n^-5)/(color(blue)(5)m^-4n^-2) = (-5m^5n^-5)/(m^-4n^-2)`

We can now use these two rules of exponents to simplify the `m` and `n` terms:

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

`(-5m^color(red)(5)n^color(red)(-5))/(m^color(blue)(-4)n^color(blue)(-2)) = (-5m^(color(red)(5)-color(blue)(-4)))/n^(color(blue)(-2)-color(red)(-5)) = (-5m^(color(red)(5)+color(blue)(4)))/n^(color(blue)(-2)+color(red)(5)) = (-5m^9)/n^3`