You need more ()s if you mean
(64r^3s^-12)/(12r^-9s^-12) times (120r^6)/(24s^-18)
If so
(64*120)r^(3+9+6)s^(-12+12+18)/(12*24) =
(80/3)*r^18*s^18
And you are close except you seem to have changed an s into an r and it is better to leave an improper fraction.
BTW: 4*8/4*2 means 4*8*2/4 = 16
(4*8)/(4*2) means 32/8 = 4
which is why you need those ()s
I thought when there was a s^-12 over s^-12 that they would cross each other out? and when you would write the answr to this question should it be like this
80/3 r^18 s^18 or 80r^18 s^18/3 ?
They do indeed cancel each other (-12+12...
but you have that s^18 at the end.
s^(-12+12+18)
They mean the same. It is usually best to keep the same types together. You might even type it as
(80/3)*r^18*s^18
even though these ()s are not necessary I think they increase the clarity. It is much better to have too many than just enough and ever so much better than not enough.
Notice what you did with
80/3 r^18 s^18
Under the rules it is correct but the way you have been doing it till now you would have meant
80/(3*r^18*s^18). Look at your very first expression. We had to guess what you meant.
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