Question

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

Answer 1

`32`

Explanation:

`(8)(-2^2)`

`:.(8)(-2*-2)`

`:.(8)(4)`

`:.8xx4=32`

Answer 2

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:

`color(green)((8))color(purple)((-2^2))`

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.

`color(green)(8)color(purple)((-2^2))`

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:

`color(green)(8)color(purple)((4))`

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

`color(green)(8)color(purple)((4))=color(green)(8)xxcolor(purple)((4))`

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

`color(green)(8)xxcolor(purple)(4)`

The next step is multiplication:

`color(green)(8)xxcolor(purple)(4)=32`

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