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6-1-57 division of monomials
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    When doing this kind of problem, we need to remember that the division is really telling us that we're going to multiply by the reciprocal of the second term. So we're going to have 18X to the fifth over 2 I'd in the ninth sometimes taught called skip, flip and multiply. So we're going to skip the first one, we're going to flip the second one and then we're going to do our operation of multiplication. So now what we're going to do is we're just going to look at each piece. So we have this 18 here and we know that this 18 can reduce with that two because two goes into 18-9 times. So we could think of this as 9X to the fifth over one Y to the 9th. Now if we wanted to, we're going to continue to reduce. So now we could see that this nine here anywhere on top can reduce with anywhere on bottom. So 9 and 81 reduce. So now we're going to have the nine goes into nine one times. So we'd have 1X to the fifth over one wide in the ninth times 6 Y to the 4th and nine goes into 81 nine times. Continuing on with the same method, this six and this nine are both reducible by three. So if we continue along, we get 1X to the fifth over one Y to the ninth. Times 6 / 3 is 2 and 9 / 3 is 3. So now we have all of the coefficients reduced and we know that one times anything is really just itself. So now we're going to look at the variables. If I have X to the fifth on top and X ^2 on bottom, that means there's 5X's on top 12345 and there were two X's down here. So we're going to be able to reduce two of the X's on top with two of the X's on bottom. I'm starting to second guess writing these all out, but I wanted to visually show you what's going on 3678, squeeze one more in. So two of these on bottom are going to cancel with two of them on top. A different way to do it is just to subtract 5 -. 2 is going to leave us this remaining three that's on top. So we're going to end up with two X squared, this two here or sorry, two X ^3 that two here, and then there's 3X's on top. Now the Y's, there's 1234 here and we're going to cancel with 1234 down here. So the bottom is going to end up being 3 Y to the fifth. One method to do it is when the variables are the same, look at which one's bigger and that's where it's going to end up. So nine was bigger than four. So we're going to have the leftover Y's in the bottom and 9 -. 4 was the five. Hope this helps.