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

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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)

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