Exercise 3 Page 271

According to the order of operations, expressions inside parentheses are evaluated first, while addition and subtraction are evaluated last. For the given expression, this means evaluating what is inside the brackets completely before adding the product. - 7+16 ÷ 2^4 + (10-4^2)

Notice also that even within this parenthetical expression, we must obey the order of operations. 10-4^2 We must remember to evaluate the exponent first, multiply next, and finally divide their results.

Operation	Before Simplification	After Simplification
Calculate power	- 7+16 ÷ 2^4 + (10-4^2)	- 7+16 ÷ 2^4 + (10- 16)
Subtract term	- 7+16 ÷ 2^4 + ( 10- 16)	- 7+16 ÷ 2^4 + (- 6)
Calculate power	- 7+16 ÷ 2^4 + (- 6)	- 7+16 ÷ 16 + (- 6)
Divide by 16	- 7+ 16 ÷ 16 + (- 6)	- 7+ 1+ (- 6)
Add and subtract terms	- 7+ 1+ ( - 6)	- 12

The expression equals - 12.

Alternative Solution

Using a Calculator

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