Question

I really need help with this

Answer 1

`(1)/(x^2y^6)`

Explanation:

We are given
`(xy^3)^2 \cdot (xy^3)^(-4)`

First rule I'm going to use is
`(m^rn^p)^s=m^(r \cdot s)n^(p \cdot s)`.

This gives us:

`(xy^3)^2 \cdot (xy^3)^(-4)` is

`(x^2y^6) \cdot (x^(-4)y^(-12))`.

Now pair up the bases that are the same:

`(x^2x^(-4)) \cdot (y^6y^(-12))`.

Add the exponents when multiplying if the bases are the same:

`x^(-2) \cdot y^(-6)`

Now usually teachers don't like negative exponents.

To get rid of the negative exponents just take the reciprocal:

`(1)/(x^2) \cdot (1)/(y^6)`

`(1)/(x^2y^6)`