Subtracting Exponents when Dividing Like BasesDate: 01/21/2005 at 16:36:27 From: snarles Subject: my question is about simplifying variables I need to simplify x to the seventh power over x to the third power. I think I should divide 7 by 3 and put that as the power, but I end up with x to the 2.3 repeating power, and the book says it's x to the fourth power. Date: 01/21/2005 at 18:10:11 From: Doctor Achilles Subject: Re: my question is about simplifying variables Hi Snarles, Thanks for writing to Dr. Math. So your problem is: x to the seventh ------------------ x to the third Now, remember that x to the seventh is shorthand for x*x*x*x*x*x*x (The * is a multiplication symbol.) So your problem is really: x*x*x*x*x*x*x --------------- x*x*x Ok, so the first step in reducing a fraction is to find a common factor in the top and bottom. One common factor is x: x*(x*x*x*x*x*x) ----------------- x*(x*x) Now we cancel out the common factor and we are left with: x*x*x*x*x*x ------------- x*x Now find another common factor: x*(x*x*x*x*x) --------------- x*(x) And we get: x*x*x*x*x ----------- x And again, we find a common factor: x*(x*x*x*x) ------------- x*(1) And we get: x*x*x*x --------- 1 Or just: x*x*x*x Or just: x to the fourth power So that is the answer. You may have heard the rule "When you divide like bases with exponents, subtract the powers" or something like that. What that means is when you have something like: x to the seventh ------------------ x to the third Your answer will be x to the (7-3) Or: x to the fourth Hope this helps. If you have other questions or you'd like to talk about this some more, please write back. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/ |
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