The document discusses exponents and properties of exponents. It provides examples of simplifying expressions with exponents, including expressions with zero and negative exponents. It also covers the multiplication property of exponents, which states that when multiplying powers of the same base, the exponents are added. So for example, am × an = am+n.

1. 8-1 Zero and Negative Exponents
& 8-3 Multiplication Properties
of Exponents
Day 38
Objective: 1.01

2. Investigation:
 23 = 2 . 2 . 2 = Do you see a
 22 = 2 . 2 = pattern?
 21 = 2 Keep it going!
 20 =
 2-1 =
 2-2 =
 2-3 =

3. Notes
Exponents Zero as an Exponent
a0 = 1
2x3
Negative Exponent
2 is the coefficient, a-1 =
x is the base and
1
3 is the exponent
a

4. Examples: Simplify
n 3-4 5) (-5)0
n (-4)-3 6) 3ab-2
n -3-2 7) 1
−3
x
n ½ -3 8) −6
5x
y

5. Examples
Evaluate if n = -2 and w = 5.
−1
9) n-3w0 11) n 2
w
0
10) w 12) 1
−2
4
n nw

6. Multiplying Powers with the SAME BASE
 23 . 24 =
WRITE IT OUT
 4 . 43 . 42 = IN EXPANDED
FORM!

7. Notes
Multiplying Powers of the Same Base
am • an = am+n

8. Examples
Rewrite using each base only once.
13) 53 x 56
14) 24 x 2-3
15) 7-3 x 72 x 76

9. Examples
Simplify
16) a • a5 19) a • b • a5
17) n2 • n3 • 7n 20) 2y3 • 7x2 • 2y4
18) 6y2 • 3y3 • 2y-4 21) m2 • n-2 • 7m