# Simplify and express it in rational form with positive exponents. (((6x^3)^2(6y^3))/((9xy)^6))?

Feb 14, 2018

The answer is $\frac{8}{19683 {y}^{3}}$.

#### Explanation:

You have to use the power of a product rule:

${\left(x y\right)}^{a} = {x}^{a} {y}^{a}$

Here's the actual problem:

$\frac{{\left(6 {x}^{3}\right)}^{2} \left(6 {y}^{3}\right)}{{\left(9 x y\right)}^{6}}$

$\frac{\left({6}^{2} {\left({x}^{3}\right)}^{2}\right) \left(6 {y}^{3}\right)}{{\left(9 x y\right)}^{6}}$

$\frac{\left(36 {x}^{6}\right) \left(6 {y}^{3}\right)}{{\left(9 x y\right)}^{6}}$

$\frac{216 {x}^{6} {y}^{3}}{{\left(9 x y\right)}^{6}}$

$\frac{216 {x}^{6} {y}^{3}}{{9}^{6} {x}^{6} {y}^{6}}$

$\frac{216 {x}^{6} {y}^{3}}{531441 {x}^{6} {y}^{6}}$

$\frac{8 \textcolor{red}{\cancel{\textcolor{b l a c k}{{x}^{6}}}} {y}^{3}}{19683 \textcolor{red}{\cancel{\textcolor{b l a c k}{{x}^{6}}}} {y}^{6}}$

$\frac{8 \textcolor{red}{\cancel{\textcolor{b l a c k}{{y}^{3}}}}}{531441 {y}^{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} 3}}$

$\frac{8}{19683 {y}^{3}}$

Unfortunately, this big fraction can't be simplified any further.