Question

How do you simplify `(x^3y^4)/( x^9y^2)` using only positive exponents?

Answer 1

`y^2/x^6`

Explanation:

If we expand `(x^3y^4)/(x^9y^2)`

We see that the number of variables in the fraction become

`(x*x*x*y*y*y*y)/(x*x*x*x*x*x*x*x*x*y*y)`

We can now cancel the similar variables

`(cancel(x*x*x)*cancel(y*y)*y*y)/(cancel(x*x*x)*x*x*x*x*x*x*cancel(y*y))`

We are left with

`(y*y)/(x*x*x*x*x*x)`

Which becomes

`y^2/x^6`

Or by using the properties of exponents

We can change `(x^3y^4)/(x^9y^2)` to

`x^3x^-9y^4y^-2`

Which becomes

`x^(3-9)y^(4-2)`

Which becomes
`x^-6y2`

Eliminating the negative exponent by placing it in the denominator we get

`y^2/x^6`