3. Martin-Gay, Beginning Algebra, 5ed 33 Exponents that are natural numbers are shorthand notation for repeating factors. 3 4 = 3 3 3 3 3 is the base 4 is the exponent (also called power) Note by the order of operations that exponents are calculated before other operations.

4. Martin-Gay, Beginning Algebra, 5ed 44 Evaluate each of the following expressions. 3434 = 3 3 3 3= 81 (–5) 2 = (– 5)(–5)= 25 –6 2 = – (6)(6)= –36 (2 4) 3 = (2 4)(2 4)(2 4)= 8 8 8= 512 3 4 2 = 3 4 4= 48 Example: a) b) c) d) e)

5. Martin-Gay, Beginning Algebra, 5ed 55 Simplify each of the following expressions. 3 2 · 3 4 = 3 6 = (3 · 3) · (3 · 3 · 3 · 3)= 729 = 3 2+4 Example: 3 2 · 3 4 = 3 6 = 729 x 4 · x 5 = x 4+5 z 3 · z 2 · z 5 = z 3+2+5 (3y 2 )(– 4y 4 )= 3 · y 2 (– 4) · y 4 = 3(– 4)(y 2 · y 4 ) = – 12y 6 = x 9 = z 10 a) b) c) d)

6. Martin-Gay, Beginning Algebra, 5ed 66

7. 77 Simplify the following expressions. Example: a) b) c) d)

8. Martin-Gay, Beginning Algebra, 5ed 88

9. 99 Simplify each of the following expressions. (2 3 ) 3 = 2 9 = 512 (x4)2(x4)2 = x 8 = 2 3·3 = x 4·2 Example: a) b)

10. Martin-Gay, Beginning Algebra, 5ed 10

11. Martin-Gay, Beginning Algebra, 5ed 11 a) b)

12. Martin-Gay, Beginning Algebra, 5ed 12

13. Martin-Gay, Beginning Algebra, 5ed 13 a) b)

14. Martin-Gay, Beginning Algebra, 5ed 14

15. Martin-Gay, Beginning Algebra, 5ed 15 a) b) c)

16. Martin-Gay, Beginning Algebra, 5ed 16