I have to simplify this and im totally confused step by step help would be so much appreciated!
$\displaystyle
\left( \frac {-6x^2y}{2xy^3} \right)^3
$
Have you made any attempt at the problem? You should be familiar with these properties of exponentiation:
$\displaystyle (ab)^n=a^nb^n$
$\displaystyle \left(\frac ab\right)^n=\frac{a^n}{b^n}$
$\displaystyle a^{-n}=\frac1{a^n}$
$\displaystyle a^ma^n=a^{m+n}$
$\displaystyle \frac{a^m}{a^n}=a^{m-n}$
(where $\displaystyle a,\,b,\,m$ and $\displaystyle n$ have values such that the above expressions are defined)
Note that a variable without an exponent can be thought of as being raised to the 1st power.
$\displaystyle \left(\frac{-6x^2y}{2xy^3}\right)^3$
$\displaystyle =\frac{-216x^6y^3}{8x^3y^9}$
$\displaystyle =\frac{-216}{8}\cdot\frac{x^6}{x^3}\cdot\frac{y^3}{y^9}$
$\displaystyle =\frac{-27\cdot8}{8}\cdot\frac{x^6}{x^3}\cdot\frac{y^3}{y^ 9}$
Now can you see how to continue?