# How do you simplify (8)(-2^2)?

Apr 17, 2018

$32$

#### Explanation:

$\left(8\right) \left(- {2}^{2}\right)$

$\therefore \left(8\right) \left(- 2 \cdot - 2\right)$

$\therefore \left(8\right) \left(4\right)$

$\therefore 8 \times 4 = 32$

Apr 17, 2018

Use PEMDAS and you will find that the simplified value is 32.

#### Explanation:

Let's use PEMDAS, which is an abbreviation for:

P arentheses
E xponents
M ultiplication
D ivision
A ddition
S ubtraction

This is the order of operations when working with mathematical expressions. Starting from the top, we have two elements in parentheses:

$\textcolor{g r e e n}{\left(8\right)} \textcolor{p u r p \le}{\left(- {2}^{2}\right)}$

Our first element is as simplified as can be, so we can remove the parentheses. The second element needs some work, so we'll start with that.

$\textcolor{g r e e n}{8} \textcolor{p u r p \le}{\left(- {2}^{2}\right)}$

Inside the parentheses, we don't have any subsets of parentheses, so we'll skip straight down to exponents. The square of any negative number is positive, which includes this scenario:

$- {2}^{2} = 4$

Replacing this in the original expression:

$\textcolor{g r e e n}{8} \textcolor{p u r p \le}{\left(4\right)}$

Now, when you have a number right next to a parentheses, it is the same as saying it is multiplied by the outer value:

$\textcolor{g r e e n}{8} \textcolor{p u r p \le}{\left(4\right)} = \textcolor{g r e e n}{8} \times \textcolor{p u r p \le}{\left(4\right)}$

Let's remove the parentheses on the 4, since it's in the simplest form, and work further down the order of PEMDAS:

$\textcolor{g r e e n}{8} \times \textcolor{p u r p \le}{4}$

The next step is multiplication:

$\textcolor{g r e e n}{8} \times \textcolor{p u r p \le}{4} = 32$

Now, we're at our simplest form since there are no more operations to do. The expression has been fully simplified.