SOLUTION: i dont understand how to do this problem!! it involves letters and numbers being the exponent can someone help me out?? a^2m b^m+1 /(over) a^m b

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: i dont understand how to do this problem!! it involves letters and numbers being the exponent can someone help me out?? a^2m b^m+1 /(over) a^m b      Log On


   

Question 91520This question is from textbook algebra and trigonometry
: i dont understand how to do this problem!! it involves letters and numbers being the exponent can someone help me out?? a^2m b^m+1 /(over) a^m b This question is from textbook algebra and trigonometry

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The key to simplifying this kind of expression is to recall that when multiplying bases with exponents, you add the exponents and when dividing bases with exponents, you subtract exponents.
Here's an example or two:
Multiplying bases with exponents:
%283%5E2%29%283%5E4%29+=+3%5E%28%282%2B4%29%29 = 3%5E6 Here, the 3 is the base.
Dividing bases with exponents:
%285%5E4%29%2F%285%5E3%29+=+5%5E%28%284-3%29%29 = 5%5E1+=+5
Now let's apply this to your problem:
a%5E%282m%29b%5E%28%28m%2B1%29%29%2F%28a%5Em%2Ab%29
Let's look at the base a first:
a%5E%282m%29%2Fa%5Em+=+a%5E%28%282m-m%29%29 = a%5Em
Now for the base b:
%28b%5E%28%28m%2B1%29%29%29%2Fb Remember that the exponent in b is 1, so you have:
b%5E%28%28m%2B1%29%29%2Fb+=+b%5E%28%28m%2B1-1%29%29 = b%5Em
Putting it all together, you get:
a%5E%282m%29b%5E%28%28m%2B1%29%29%2F%28a%5Em%2Ab%29+=+a%5Em%2Ab%5Em