# How do you simplify (2y^3*3xy^3)/(3x^2y^4) and write it using only positive exponents?

May 4, 2017

$\frac{2 {y}^{3} \cdot 3 x {y}^{3}}{3 {x}^{2} {y}^{4}} = \textcolor{b l u e}{\frac{2 {y}^{2}}{x}}$

#### Explanation:

Simplify:

$\frac{2 {y}^{3} \cdot 3 x {y}^{3}}{3 {x}^{2} {y}^{4}}$

Gather like terms.

$\frac{2 \cdot 3 x {y}^{3} {y}^{3}}{3 {x}^{2} {y}^{4}}$

Divide whole numbers.

$\frac{6 x {y}^{3} {y}^{3}}{3 {x}^{2} {y}^{4}}$

Simplify.

$\frac{2 x {y}^{3} {y}^{3}}{{x}^{2} {y}^{4}}$

Apply the product rule of exponents: ${a}^{m} \cdot {a}^{n} = {a}^{m + n}$

$\frac{2 x {y}^{3 + 3}}{{x}^{2} {y}^{4}}$

Simplify.

$\frac{2 x {y}^{6}}{{x}^{2} {y}^{4}}$

Apply the quotient rule of exponents: "a^m/a^n=a^(m-n) Recall that a variable without an exponent is understood to be raised to the 1st power.

$2 {x}^{1 - 2} {y}^{6 - 4}$

Simplify.

$2 {x}^{- 1} {y}^{2}$

Apply the negative exponent rule: ${a}^{- m} = \frac{1}{a} ^ m$.

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