Question

How do you divide `(-15x)^7 / (25x)^9`?

Answer 1

There are probably many ways to express this result; my version is
`color(white)("XXXX")` `-3^7/(5^5x^2)`

Explanation:

`((-15x)^7)/((25x)^9)`

`color(white)("XXXX")` `=((-15)^7)/((25)^9) * (x^7)/(x^9)`

`color(white)("XXXX")` `=((-15)^7)/((25)^7) * 1/(25^2) * (x^7)/(x^9)`

`color(white)("XXXX")` `=((-15)/25)^7 * 1/(25^2) * (1)/(x^2)`

`color(white)("XXXX")` `=(-3/5)^7*1/((5^4x^2)`

`color(white)("XXXX")` `=-3^7/(5^5x^2)`