Question

How do you simplify `(e^3f^9)/(e^7f^3)`?

Answer 1

See the entire simplification process below:

Explanation:

Solution 1) Use this rule for exponents:

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

`(e^color(red)(3)f^color(red)(9))/(e^color(blue)(7)f^color(blue)(3)) = e^(color(red)(3)-color(blue)(7))f^(color(red)(9)-color(blue)(3)) = e^-4f^6`

Solution 2) Use these rules for exponents if you do not want negative exponents:

`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))`

`(e^color(red)(3)f^color(red)(9))/(e^color(blue)(7)f^color(blue)(3)) = f^(color(red)(9)-color(blue)(3))/e^(color(blue)(7)-color(red)(3)) = f^6/e^4`