Question

12x^ay^b / ( - 6x^ay )

Answer 1

`-2y^(b-1)`

Explanation:

`(12x^ay^b)/(-6x^ay)`

In multiplication of fractions you can do this:

`(a)/(c) \cdot (b)/(d)=(a \cdot b)/(c \dot d) \text{ or the other way around } (a \cdot b)/(c \dot d)=(a)/(c) \cdot (b)/(d)`.

So that is exactly what we are going to do here:

`(12x^ay^b)/(-6x^ay)`

`(12)/(-6) \cdot (x^a)/(x^a) \cdot (y^b)/(y)`

We know that 12 divided by -6=12/-6 =-2.

We also know assuming x isn't 0 that x^a/x^a=1.

On the last fraction, the only thing you can do there to simplify is use the following law of exponents:
`(v^m)/(v^n)=v^(m-n)`.

So we have

`(12x^ay^b)/(-6x^ay)`

`(12)/(-6) \cdot (x^a)/(x^a) \cdot (y^b)/(y)`

`(-2) \cdot (1) \cdot (y^(b-1))`

Simplifying a bit and leaving out the ( ).

`-2y^(b-1)`