Cancelling ExponentsDate: 03/04/97 at 19:03:24 From: Philip Powell Subject: Multiplying nasty fractions Hello, How did they turn 2^29 x 3^16 3 ------------ into --- ? 2^32 x 3^15 2^3 Any help would be greatly appreciated. I do have one other question though: How do you do this for free? Our family is quite amazed that you have the time to answer all of these questions and that you do it for no charge. (That's not a complaint, mind you!) Date: 03/04/97 at 23:40:21 From: Doctor Mike Subject: Re: Multiplying nasty fractions Hello, Think about this formula: A X A*X --- * --- = ----- B Y B*Y In a way that's really all you need, together with the definition of exponent, and the fact that N/N = 1. 2^29 x 3^16 2^29 3^16 2^29 1 3^15 3 ----------- = ---- x ---- = ---- x --- x ---- x --- 2^32 x 3^15 2^32 3^15 2^29 2^3 3^15 1 Now anything where the numerator equals the denominator just disappears because it is the same as multiplying by one, so that long expression to the right above equals: 1 3 1 3 3 3 1 x --- x 1 x --- = --- x --- = --- = --- 2^3 1 2^3 1 2^3 8 The safest way to work complicated problems like this is to take lots of "small steps" which you know are correct because of some really basic principles. I should tell you that there are some "shortcuts" or "tricks" to doing this kind of problem faster. You might hear someone say something like "JUST CANCEL THE 2^29 INTO THE 2^32 LEAVING EIGHT IN THE DENOMINATOR". There is nothing wrong with that if you really know what you are doing. But if you are a little bit unsure or rusty, you can get into trouble that way. I don't answer Dr. Math questions for a living. It's sort of a hobby. Besides, I think it's good to volunteer your efforts as you can. I am not the only mathematician on staff here. There's quite a bunch of us, all with different interests. Even so, we don't get to all the questions. That's too bad because some question we don't get to might be from a student who is really struggling, or from a young genius needing to be taken seriously and given encouragement. Anyway, enough philosophy. I hope you got what you need. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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