Question

How do you simplify `(c^8d^-12)/(c^-4d^-8)`?

Answer 1

See the entire simplification process below:

Explanation:

To simplify this expression we will use this rule of exponents:

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

`(c^color(red)(8)d^color(red)(-12))/(c^color(blue)(-4)d^color(blue)(-8)) -> c^(color(red)(8)-color(blue)(-4))d^(color(red)(-12)-color(blue)(-8)) -> c^(color(red)(8)+color(blue)(4))d^(color(red)(-12)+color(blue)(8)) -> c^12d^-4`

If we want to have only positive exponents we can use this rule of exponents:

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

`c^12d^color(red)(-4) -> c^12/d^color(red)(4) -> c^12/d^4`