1. Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 1 Introduction to Algebraic Expressions

2. 1-2 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Exponential Notation and Order of Operations Exponential Notation Order of Operations Simplifying and the Distributive Law The Opposite of a Sum 1.8

3. 1-3 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Exponential Notation The 5 is called an exponent. The 4 is the base.

4. 1-4 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Write exponential notation for 7  7  7  7  7  7. Solution Exponential notation is 7 6 7 is the base. 6 is the exponent.

5. 1-5 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Evaluate a) 8 2 b) (−8) 3 c) (4y) 3 Solution a) 8 2 = 8  8 = 64 b) (−8) 3 = (−8) (−8) (−8) = 64(−8) = − 512

6. 1-6 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example c) (4y) 3 = (4y) (4y) (4y) = 4  4  4  y  y  y = 64y 3

7. Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Exponential Notation For any natural number n,

8. Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Rules for Order of Operations 1. Simplify, if possible, within the innermost grouping symbols, ( ), [ ], { }, | |, and above or below any fraction bars. 2. Simplify all exponential expressions. 3. Perform all multiplications and divisions, working from left to right. 4. Perform all additions and subtractions, working from left to right.

9. 1-9 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Simplify: Solution Multiplying Subtracting and adding from left to right

10. 1-10 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Evaluate  16  8(7  y) 2 for y = 2. Solution  16  8(7  y) 2 =  16  8(7  2) 2 =  16  8(5) 2 =  16  8(25) =  2(25) =  50

11. 1-11 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Simplify: Solution

12. 1-12 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Simplify: Solution

13. 1-13 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Simplify: Solution Distributive Law Combining Like Terms

14. 1-14 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Write an expression equivalent to  (4x + 3y + 5) without using parentheses. Solution  (4x + 3y + 5) =  1(4x + 3y + 5) =  1(4x) +  1(3y) +  1(5) =  4x  3y  5

15. Copyright © 2014, 2010, and 2006 Pearson Education, Inc. The Opposite of a Sum For any real numbers a and b, −(a + b) = −a + (−b) = −a − b (The opposite of a sum is the sum of the opposites.)

16. 1-16 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Simplify: Solution

17. 1-17 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Simplify: Solution