Question

How do you express `(12x^-5y^5)/(24x^3y^-2)` in simplest form, using only positive exponents?

Answer 1

See the entire simplification process below:

Explanation:

First, rewrite this expression as:

`(12/24)(x^-5/x^3)(y^5/y^-2) = 1/2(x^-5/x^3)(y^5/y^-2)`

Now, use these rules for exponents to simplify the `x` and `y` 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))`

`1/2(x^color(red)(-5)/x^color(blue)(3))(y^color(red)(5)/y^color(blue)(-2)) = 1/2(1/x^(color(blue)(3)-color(red)(-5)))(y^(color(red)(5)-color(blue)(-2)))=`

`1/2(1/x^(color(blue)(3)+color(red)(5)))(y^(color(red)(5)+color(blue)(2))) = 1/2(1/x^8)(y^7) =`

`y^7/(2x^8)`