Simplifying fractions with variables and exponents

[Acecustis]

Okay well the problem is:

3x^2y/x^3

The answer to the problem is 3y/x. My question is how to come up with this answer. I'm sure this is simple and there was a time many years ago I could do this equation, but I can't for the life of me remember the rule concerning exponents in the denominator. Please help!

 

[Idealistic]

so, you have 3x^2*y/x^3

or look at it like this:

(3*x*x*y)/(x*x*x)

if you cancel the two x's in the numerator, you're left with one x left in the denominator like so

3*y/x

its the same as

8/2 = (2*2*2)/2 = 2*2 = 4 (after I cancel one of the two's in the numerator)

or you can just use the method of adding exponents when you multiply and subtracting exponents when you divide, like:

3*y^3/y^2 = 3*y (3-2 in the exponents) or 3*y^2/y^5 = 3/y^3 (2-5 in the exponents)

 

[Acecustis]

Thanks for the easy to understand explanation!

 

[kanishkporwal]

While simplifying fractions, many things have to be kept in mind
usually the problems are not so simple like the one you wrote above.So we have to look any thing that can be taken out as a common factor from both numerator and denominator.