Exercise 12 Page 256

According to the order of operations, expressions inside parentheses are evaluated first, followed by exponents, then multiplication and division, and finally addition and subtraction are evaluated last. We can use the acronym PEMDAS to help us remember the correct order! For the given expression, this means evaluating the expression inside the square brackets completely before performing the product.

4 * [ 3 + 3(20 - 4^2-2 )] Notice also that even within this parenthetical expression, we must follow the order of operations. 3 + 3(20 - 4^2-2 ) Let's do it!

Operation	Before Simplification	After Simplification
Calculate power	4 * [ 3 + 3(20 - 4^2-2 )]	4 * [ 3 + 3(20 - 16-2 )]
Subtract terms	4 * [ 3 + 3( 20 - 16- 2 )]	4 * [ 3 + 3( 2 )]
Multiply	4 * [ 3 + 3( 2 )]	4 * [ 3 + 6 ]
Add terms	4 * [ 3 + 6 ]	4 * [ 9 ]
Multiply	4 * [ 9 ]	36

The expression is equal to 36.

Alternative Solution

Using a Calculator

We can also evaluate this expression using a calculator. To do so, we type it as shown below.

Whenever using a calculator for a complicated expression such as this, be very careful when placing the parentheses. A calculator will only do what it is told to do, not what you meant for it do.