# How do you evaluate \frac { 10+ 2( - 5) ^ { 2} } { ( 2^ { 2} ) ( 3) }?

Dec 30, 2016

$\frac{10 + 2 \left(- 5\right)}{\left({2}^{2}\right) \left(3\right)} = \textcolor{g r e e n}{5}$

#### Explanation:

Using P E DM AS
Evaluate:
$\textcolor{w h i t e}{\text{XXX}}$Parentheses first
$\textcolor{w h i t e}{\text{XXXXXX}}$for the given example
$\textcolor{w h i t e}{\text{XXXXXX}}$parentheses are only used to clarify multiplication.
$\textcolor{w h i t e}{\text{XXX}}$Exponentiation next
$\textcolor{w h i t e}{\text{XXX}}$Division and Multiplication next (left to right)
$\textcolor{w h i t e}{\text{XXX}}$Addition and Subtraction last (left to right)

Because of the "left-to-right" requirement we will first convert the given expression into a linear form:
$\textcolor{w h i t e}{\text{XXX}} \frac{10 + 2 {\left(- 5\right)}^{2}}{\left({2}^{2}\right) \left(3\right)}$
$\textcolor{w h i t e}{\text{XXXXXX}} = \left(10 + 2 {\left(- 5\right)}^{2}\right) \div \left(\left({2}^{2}\right) \left(3\right)\right)$

$\textcolor{w h i t e}{\text{XXXXXX}} = \left(10 + 2 \cdot 25\right) \div \left(\left({2}^{2}\right) \left(3\right)\right)$

$\textcolor{w h i t e}{\text{XXXXXX}} = \left(10 + 50\right) \div \left(\left({2}^{2}\right) \left(3\right)\right)$

$\textcolor{w h i t e}{\text{XXXXXX}} = 60 \div \left(\left({2}^{2}\right) \left(3\right)\right)$

$\textcolor{w h i t e}{\text{XXXXXX}} = 60 \div \left(4 \cdot 3\right)$

$\textcolor{w h i t e}{\text{XXXXXX}} = 60 \div 12$

$\textcolor{w h i t e}{\text{XXXXXX}} = 5$