# How do you simplify \frac { 3^ { 2} \cdot 3^ { 3} } { 2^ { 2} \cdot 3^ { 4} }?

Jan 15, 2018

See a couple of process below:

#### Explanation:

First Process:

We can use this rule of exponents to combine the terms in the numerator:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$\frac{{3}^{\textcolor{red}{2}} \cdot {3}^{\textcolor{b l u e}{3}}}{{2}^{2} \cdot {3}^{4}} \implies$

${3}^{\textcolor{red}{2} + \textcolor{b l u e}{3}} / \left({2}^{2} \cdot {3}^{4}\right) \implies$

${3}^{5} / \left({2}^{2} \cdot {3}^{4}\right)$

We can now use these rules of exponents to complete the simplification of the $3$ terms:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$ and ${a}^{\textcolor{red}{1}} = a$

${3}^{\textcolor{red}{5}} / \left({2}^{2} \cdot {3}^{\textcolor{b l u e}{4}}\right) \implies$

${3}^{\textcolor{red}{5} - \textcolor{b l u e}{4}} / {2}^{2} \implies$

${3}^{\textcolor{red}{1}} / {2}^{2} \implies$

$\frac{3}{2} ^ 2 \implies$

$\frac{3}{4}$

Second Process:

$\frac{{3}^{2} \cdot {3}^{3}}{{2}^{2} \cdot {3}^{4}} \implies \frac{9 \cdot 27}{4 \cdot 81} \implies \frac{3 \cdot 3 \cdot 27}{4 \cdot 81} \implies \frac{3 \cdot 81}{4 \cdot 81} \implies \frac{3 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{81}}}}{4 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{81}}}} \implies \frac{3}{4}$