# How do you simplify {2-4[3+(5+1/2)^2]}-7?

Sep 18, 2016

$- 138$

#### Explanation:

In mixed operation calculations, always count the number of terms first. Each term must simplify to a single number.

Within each term, the order of operations is brackets first , then from strongest to weakest operations,
Powers and roots
Multiply and divide

Add and subtract is done last from left to right

$\left\{2 - 4 \left[3 + {\left(\textcolor{red}{5 + \frac{1}{2}}\right)}^{2}\right]\right\} - 7 \text{ } \leftarrow$ there are 2 terms

=$\left\{2 - 4 \left[3 + \textcolor{red}{{\left(\frac{11}{2}\right)}^{2}}\right]\right\} - 7 \text{ } \left(\rightarrow 5 + \frac{1}{2} = 5 \frac{1}{2} = \frac{11}{2}\right)$
=$\left\{2 \textcolor{red}{- 4 \left[3 + \frac{121}{4}\right]}\right\} - 7 \text{ } \leftarrow$distributive law with -4
=$\left\{2 - \textcolor{red}{12 - 121}\right\} - 7$
=$- 131 - 7$
=$- 138$