Question

I really need help with this

Answer 1

Answer:

$\frac{1}{x^2y^6}$

Step-by-step 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:

$\frac{1}{x^2} \cdot \frac{1}{y^6}$

$\frac{1}{x^2y^6}$