Question

How do you simplify `(16q^0 r^-6) /( 4q^-3 r^-7)`?

Answer 1

`(16q^0r^(-6))/(4q^(-3)r^(-7))=4q^3r`

with exclusions `q!=0` and `r!=0`

Explanation:

If `a != 0` and `b` and `c` are integers, then `a^b/a^c = a^(b-c)`

So:

`(16q^0r^(-6))/(4q^(-3)r^(-7))`

`=(16/4)(q^0/q^(-3))(r^(-6)/r^(-7))`

`=4 q^(0-(-3)) r^((-6)-(-7))`

`=4q^3r^1`

`=4q^3r`

with exclusions `q!=0` and `r!=0`

The exclusions are required since if `q=0` or `r=0` then at least one of `q^(-3)`, `r^(-6)`, `r^(-7)` is undefined.