Question

How do you simplify `(525x^5y^4w )/(630 x^4y^5z)`?

Answer 1

`(5xw)/(6yz)`

Explanation:

Given: `(525 x^5 y^4 w)/(630 x^4 y^5 z)`

One way to simplify is to use the exponent rules:

`x^m/x^n = x^(m-n) " and " x^-1 = 1/x`

`(525 x^5 y^4 w)/(630 x^4 y^5 z) = (5x^(5-4)y^(4-5)w)/(6z) = (5xy^-1w)/(6z) = (5xw)/(6yz)`

A second way is to find the greatest common factor (GCF) in both the numerator and the denominator and cancel:

`525 x^5 y^4 w = 3*5*5*7*x*x*x*x*x*y*y*y*y*w`

`630 x^4 y^5 z = 2*3*3*5*7*x*x*x*x*y*y*y*y*y*w`

GCF = `3*5*7*x*x*x*x*y*y*y*y = 105x^4y^4`

Factor using the GCF and cancel:

`(525 x^5 y^4 w)/(630 x^4 y^5 z) = (cancel(105x^4y^4)(5xw))/(cancel(105x^4y^4)(6yz)) = (5xw)/(6yz)`