Question

Match the products of rational expressions with their simplest forms.

Answer 1

Lets simplify each one of the rational expressions using the product rule of exponents:
`a^n*a^m=a^(n+m)` and the quotient rule of exponents:
`(a^n)/(a^m) =a^(n-m)`.

1.
`(-3x^2)/(2y^2) * (y^2)/(9x) =- (x)/(6) = (-1)/(6) x`

2.
`(5y^2)/(10x^2) * (4x^2)/(y) =2y`

3.
`(-9y^2)/(5x) * (-10x^2)/(3y) =6xy`

4.
`(14x^2)/(5y) * (-10y)/(7x) =-4x`

We can conclude that you should pair the rational expressions with their simplest form as follows:

`6xy-----\ \textgreater \ (-9y^2)/(5x) * (-10x^2)/(3y)`

`(-1)/(6) x-----\ \textgreater \ (-3x^2)/(2y^2) * (y^2)/(9x)`

`-4x-----\ \textgreater \ (14x^2)/(5y) * (-10y)/(7x)`

`2y-----\ \textgreater \ (5y^2)/(10x^2) * (4x^2)/(y)`