# How do you simplify 3^5/3 and write it using only positive exponents?

Feb 15, 2017

${3}^{4}$

#### Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

Although not normally done it quite correct to write $3 \text{ as } {3}^{1}$

${3}^{5}$ is the same as ${3}^{1} \times {3}^{1} \times {3}^{1} \times {3}^{1} \times {3}^{1}$

$= {3}^{1 + 1 + 1 + 1 + 1} = {3}^{5}$

So this is also the same as ${3}^{1 + 4} = 3 \times {3}^{4}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

Write as $\frac{3 \times {3}^{4}}{3}$

This is the same as $\frac{3}{3} \times {3}^{4}$

but $\frac{3}{3} = 1$ giving

$1 \times {3}^{4} \text{ which is just } {3}^{4}$