# How do you simplify (3xy^4)/(9xy) using only positive exponents?

Apr 19, 2016

${y}^{3} / 3 \text{ or } \frac{1}{3} {y}^{3}$

#### Explanation:

Using the following$\textcolor{b l u e}{\text{ rules of exponents }}$

• a^m/a^n = a^(m-n)

$\frac{3 x {y}^{4}}{9 x y} = \frac{3}{9} \times \frac{x}{x} \times {y}^{4} / {y}^{1}$

$= \frac{1}{3} \times 1 \times {y}^{4 - 1} = \frac{1}{3} {y}^{3}$

Apr 19, 2016

## ${y}^{3} / 3$

#### Explanation:

You can separate the numerator and the denominator into three separate terms:
$\frac{3 \times x \times {y}^{4}}{9 \times x \times y}$

This will help you to divide the terms that are in like terms (such as 3 and 9, the two x's, and ${y}^{4}$ and y).

Important Key Concepts To Note:

• remember the quotient rule in exponents.
${x}^{b} / {x}^{a} = {x}^{b - a}$
• Terms that have no exponents with them, there's always an invisible "1" as the exponent.
$a = {a}^{1}$

Let's separate the terms and divide:
$\frac{3}{9} \times {x}^{1} / {x}^{1} \times {y}^{4} / {y}^{1}$
$= \frac{1}{3} \times 1 \times {y}^{3}$ which is the same thing as ${y}^{3} / 3$

Answer: $= {y}^{3} / 3$