# How do you simplify (3(x²y³)²)/((3xy³)³)?

Oct 10, 2017

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

#### Explanation:

Expand using definition of exponents:

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

Rearrange the multiplication using the commutative property:

$\frac{3 {x}^{2} {x}^{2} {y}^{3} {y}^{3}}{3 \cdot 3 \cdot 3 x \cdot x \cdot x {y}^{3} {y}^{3} {y}^{3}}$

Use product property of exponents and multiply the constants:

$\frac{3 {x}^{4} {y}^{6}}{27 {x}^{3} {y}^{9}}$

Use quotient property of exponents and divide the constants:

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