How do you simplify #(x^5y^8)/(x^4y^2)#?

Question

2643 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-02-05T12:51:52

The answer is #xy^6#

Let's see how we get there.

First the long way. You can write #y^2# as #y*y# etc.

Your formula then is:

#(x*x*x*x*x*y*y*y*y*y*y*y*y)/(x*x*x*x*y*y)#

Now cross out the #x#'s and #y#'s above and below the dividing bar two by two. You will be left with:

#x*y*y*y*y*y*y# and nothing below the bar

This can be written as #x*y^6=xy^6#

A shorter way would be to subtract the exponents:

First we rewrite: #(x^5*y^8)/(x^4*y^2)=x^5/x^4*y^8/y^2#

#x^5/x^4=x^(5-4)=x^1=x# and #y^8/y^2=y^(8-2)=y^6#

Answer: #x*y^6=xy^6# (same answer of course)