SOLUTION: How would you simplify a^2b/a^5b^3? Thanks so much.

First method: breaking everything into prime factors:

Write  as 
Write  as 
Write  as 

Then we have:



Put a  factor on the top and bottom:



Then we cancel the two 's on top with two of
the 's on the bottom:



Then we cancel the  in the top into one of the
's in the bottom:



So all that didn't cancel out is



Then write the  as  and  as 



That way will always work, but here is another method:

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Second method:



Put a 1 coefficient on top and bottom.
Also put a 1 exponent on the  on top:



Now subtract the exponents of 
That is subtract them "largest minus smaller"
and put the result where the larger exponent
was, that is, either the numerator or
denominator.

In this case the larger exponents are both in the
bottom, 

so we subtract exponents of ,
5-2 getting 3, so we put  on the
bottome because the larger exponent 5 was
on the bottom.   

we also subtract exponents of ,
3-1 getting 2, so we put  on the
bottom because the larger exponent 3 was
on the bottom.

So we have:



or

  

Edwin