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

1 Answer

#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#