Question

How do you simplify `\frac { s ^ { - 6} } { s ^ { - 5} }`?

Answer 1

`s^(-1)=1/s`

Explanation:

In this question, I think it'll be helpful to first convert the different exponents into positive ones. I'll use the rule that `x^(-1)=1/x`:

`s^(-6) / s^(-5)`

`s^5/s^6`

At this point we can do this a few different ways. One way is to see that we can write this as:

`(sxxsxxsxxsxxs)/(sxxsxxsxxsxxsxxs)` and we can cancel our way through:

`(cancel(color(red)s)xxcancel(color(blue)(s))xxcancel(color(green)s)xxcancel(color(brown)(s))xxcancel(color(orange)(s)))/(cancel(color(red)s)xxcancel(color(blue)(s))xxcancel(color(green)s)xxcancel(color(brown)(s))xxcancel(color(orange)(s))xxs)=1/s`

We can also do this by using the rule `x^a -: x^b=x^(a-b)`:

`s^(5-6)=s^(-1)=1/s`