# Question #024f4

Apr 16, 2017

See the entire solution process below:

#### Explanation:

In the standard order of operations you first, execute the terms with exponents:

$3 \cdot \frac{\textcolor{red}{{3}^{5}}}{\textcolor{b l u e}{{3}^{2}}} = 3 \cdot \frac{243}{9} = 3 \cdot 27 = 81$

Another way to evaluate this is using various rules of exponents:

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

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

Then:

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

$3 \cdot {3}^{3} = {3}^{\textcolor{red}{1}} \cdot {3}^{\textcolor{b l u e}{3}} = {3}^{\textcolor{red}{1} + \textcolor{b l u e}{3}} = {3}^{4} = 81$