8.1 zero & negative exponents. 8.1 – zero & negative exponents goals / “i can…” ...
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8.1
Zero & Negative Exponents
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
Goals / “I can…”Simplify expressions with zero and negative
exponentsEvaluate exponential expressions
1 • 1 = +1 1 • -1 = -1
-1 • -1 = +1
-1 • -1 • -1 = -1
Multiply Integers REVIEW
Odd # of Negatives = Negative Even # of Negatives = Positive
-1 • -1 • -1 • -1 = +1
-1 • -1 • -1 • -1 • -1 = -1
-1 • -1 • -1 • -1 • -1 • -1 = +1
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
22 Means… 2 • 2 = 4 21 Means… 2 = 2
20 Means… 1
What does 2-1 Mean?
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
What does 2-1 Mean? You cannot leave an exponent
negative because there is NO WAY to express it’s meaning.
You must make it positive!
11 1
22
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
You do NOT want to have negative exponents in your answer. You get rid of them by flipping the exponent over, like reciprocals.
2 51
5 2 If the negative exponent
is on top, move it to the bottom.
22
12
2 2
2
12
2 1
4 4
1
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
Definition of Negative ExponentFor any integer n, a-n is the reciprocal of an
1n
naa
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
Definition of Negative ExponentFor any integer n, a-n is the reciprocal of an
11 1
22
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
Definition of Negative ExponentFor any integer n, a-n is the reciprocal of an
22
1( 5)
( 5)
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
Simplify.11) 3
23) 5
22) 4
24) 6
13
215
125
214
116
216
136
A negative exponent is an inverse!1x 1
xFlip the number over to make the exponent positive!
1 1
1 1
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
Follow the Pattern!
210
10
10
10
10
3
4
5
100
1,00010,000
100,000
10110
110
-1 = 0.1
10-2
1
110 2
1100
= 0.01
10-3 1
10 3 11000 = 0.001
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
Zero Exponent:
Negative Exponent:
0 1a 1n
naa
RULE: YOU SHOULD NEVERNEVER HAVE A NEGATIVE EXPONENT AS YOUR FINAL
ANSWER
8.1 – Zero & Negative Exponents
01) 6
Simplify.
02) -2
03) 9 04) 5 20 8
1 1
1 1
0 1x
8.1 – Zero & Negative Exponents
8.1 – Zero & Negative Exponents
Simplify the following:
a. 3 c. (-4)
b. (-8.1) d. (2.45678913)
-2 -5
0 0
1n
naa
25) 12 26) 7 21
121
144
217
149
Simplify.
1 1
8.1 – Zero & Negative Exponents
8.1 – Zero & Negative Exponents
Simplify
a. 11m b. 7s - 4t
c. d.
-5 2
3
2a
2
5
v
n
Simplify the following expressions:
2
3
5
0
4
1.4
.3
1.2
6.1
gh
x
7
4
5
0
6
3
.8
7.
0) zfor (.6
.5
t
r
xy
z
p
n
3h
g
1
x5
16
-n3p6
1
55
1
yx
4
7
r
t
Practice Problems
1. 2-2
¼
2. (-2)0
1
3. 5-x
1/5x
4. (½)-1 2
5. 5(2-1)5/2
6. 2x-2y-3
2/y3x2
More Practice
7. x-5
1/x5
8.
x5/2
9. x4y-7
x4/y7
10.
x3y/9
521
x
1391
yx
8.1 – Zero & Negative Exponents
Evaluate each expression for n = -2 and w = 5
a. n w b. c. d. 2
1
w
n
4
0
n
w2
1nw
-3 0