1. TO MULTIPLY POWERS HAVING THE SAME BASE
OBJECTIVE
TO MULTIPLY POWERS HAVING THE SAME BASE

2. Pick up Homework and Quiz Test Chapter 3 25min max Start Chapter 5
Math 083 Bianco 2/22/10
Pick up Homework and Quiz
Test Chapter 3 25min max
Start Chapter 5

3. Today we will...
use multiplication properties of exponents to evaluate and simplify expressions.

4. BASE EXPONENT EXPONENTIAL FORM FACTORED FORM COEFFICIENT
VOCABULARY
BASE
EXPONENT
EXPONENTIAL FORM
FACTORED FORM
COEFFICIENT

5. Exponents What is an exponent? What does xn mean?
x is called the base.
n is called the exponent.
x is raised to the nth power.

6. { Exponents xn = x • x • x ....... x n factors of x x = base
n = exponent
xn = x to the nth power

7. Find numerical answers: 1)26 2) 38 3) 44 4) (22)3 5) (34)2 6) (42)2
???????????????????
Find numerical answers:
1)26 2) 38 3) 44
4) (22)3 5) (34)2 6) (42)2

8. Find numerical answers: 1)26 2) 38 3) 44 64 6561 256
???????????????????
Find numerical answers:
1)26 2) 38 3) 44
4) (22)3 5) (34)2 6) (42)2

9. Exponents
x3 • x2 =

10. Exponents
x3 • x2 = x • x • x • x • x { {

11. Exponents
x3 • x2 = x • x • x • x • x { {
3 factors
of x

12. { { Exponents x3 • x2 = x • x • x • x • x 3 factors of x 2 factors

13. { { Exponents x3 • x2 = x • x • x • x • x = x5 3 factors of x

14. Rules for Exponents Let a be any number and m and n be integers.
1. am • an =

15. Rules for Exponents Let a be any number and m and n be integers.
1. am • an = am + n

16. Rules for Exponents Let a be any number and m and n be integers
1. am • an = am + n
Write the rule in words:

17. The Product Rule Product Rule for Exponents
If m and n are positive integers and a is a real number, then
am · an = am+n
Example:
Use the product rule to simplify.
32 · 34
= 32+4
= 36
= 3 · 3 · 3 · 3 · 3 · 3
= 729
z3 · z2 · z5
= z3+2+5
= z10
(3y2)(– 4y4)
= 3 · y2 (– 4) · y4
= 3(– 4)(y2 · y4)
= – 12y6

18. Product of Powers Rules for Exponents
To multiply powers with like bases add the exponents, keep the base the same.
Product of Powers

19. Simplify
1. c8 • c10 =
c (10+8) = c 18

20. Simplify
2. b4 • b7 • b5
= b ( )
= b16

21. Keep base the same and add exponents an am = am+n
Product of powers
Keep base the same and add exponents
an am = am+n
ex: ( 3x2) (–5x4) = (3)(–5)(x2 ) (x4 ) =
-15 x6

22. Simplify: 3) (x35)(x23) 4) (43)(42) 5) (–x5)(–x7)(x3)(x2) 6) (–1)25

23. Simplify:
3) (x35)(x23) = x58
4) (43)(42)= 45
5) (–x5)(–x7)(x3)(x2) = x17
6) (–1)25 = – 1

24. b 3 b 7 = b 2 b 3 = c 6 c 5 = x 5 x = m 4 m = (x) (x) (x) =
Complete #
m 3 m 2 =
b 3 b 7 =
b 2 b 3 =
c 6 c 5 =
x 5 x =
m 4 m =
(x) (x) (x) =

25. ( c2 )3 =
( c2 ) ( c2 ) ( c2 )= c6

26. ( x 8)3 =
( x 8) ( x 8) ( x 8) =
x24

27. Zero Exponent Zero Exponent If a does not equal 0, then a0 = 1.
Example:
Simplify each of the following expressions. 50
= 1
(xyz3)0
= x0 · y0 · (z3)0
= 1 · 1 · 1 = 1
–x0
= –(x0)
= – 1

28. The Quotient Rule Quotient Rule for Exponents
If a is a nonzero real number and m and n are integers, then
Example:
Simplify the following expression.
Group common bases together

29. Negative Exponents Negative Exponents
If a is a real number other than 0 and n is a positive integer, then
Example:
Simplify by writing each of the following expressions with positive exponents or calculating.
Remember that without parentheses, x is the base for the exponent –4, not 2x

30. Assignment # 2
5.1 #’s 1, 5, 9, 13, 17, 19, 25, 27, 31, 43, 45, 47, 53, 55, 65, 69, 77, 81, 83
5.2 #’s multiples of 3 i.e. 3, 6, 9 , …

31. BASE EXPONENT EXPONENTIAL FORM FACTORED FORM COEFFICIENT
VOCABULARY
BASE
EXPONENT
EXPONENTIAL FORM
FACTORED FORM
COEFFICIENT

32. Exponents What is an exponent? What does xn mean?
x is called the _____.
n is called the _____.
x is raised to the nth ____.

33. Assignment # 2
5.1 #’s 1, 5, 9, 13, 17, 19, 25, 27, 31, 43, 45, 47, 53, 55, 65, 69, 77, 81, 83
5.2 #’s multiples of 3 i.e. 3, 6, 9 , …

34. Exponents {
xn = x • x • x x
n factors of x
x =
n =
xn =

35. Find numerical answers: 1)26 2) 38 3) 44 4) (22)3 5) (34)2 6) (42)2
???????????????????
Find numerical answers:
1)26 2) 38 3) 44
4) (22)3 5) (34)2 6) (42)2

36. Exponents
x3 • x2 =

37. Simplify
1. c8 • c10 =

38. Simplify
2. b4 • b7 • b5

39. Simplify: 3) (x35)(x23) 4) (43)(42) 5) (–x5)(–x7)(x3)(x2) 6) (–1)25

40. Keep base the same and add exponents an am = am+n ex: ( 3x2) ( -5x4) =
Product of powers
Keep base the same and add exponents
an am = am+n
ex: ( 3x2) ( -5x4) =

41. Multiply the following
1. a4 ( a3) ( a)
2. ( 3x3 ) ( -2x4 )

42. Evaluate
if x = 3 and y = -5
x3 + y4
2. Divide
(3x5y2 )/ (9x2y5)
3. Mult 3x3 (-2 x5 )