3.2 Zero and Negative Exponents
Common Core Standards
8. EE.3 Use numbers expressed in the form of a single digit times an
integer power of 10 to estimate very large or very small quantities, and to
express how many times as much one is than the other. For example,
estimate the population of the United States as 3 × 108 and the population
of the world as 7 × 109, and determine that the world population is more
than 20 times larger.
WARM-UP
Evaluate the expressions.
1) 51
2) 5 2
3) 5 3
5) 25
6) 125
Find the reciprocal.
4) 5
7) 5 3
Zero and Negative Exponents
What is the pattern?
53 = 5 i 5 i 5 = 125
2
5 = 5 i 5 = 25
51 = 5
0
5 =
5 −1 =
5 −2 =
5 −3 =
NOTES
Negative exponents are the reciprocal of the positive
exponent. They do not make anything negative.
Examples
Rewrite the power as an equivalent expression with a
positive exponent.
x −2
9 −4
7 −1
EXAMPLES
Evaluate the expressions.
2
−3
7 −2
Evaluate the expression for y = 4.
y −3
NOTES
Anything to the 0th power equals 1.
0
x =1
Concept Check
Evaluate all three expressions.
0
6
1
6
6
−1
Evaluate all three expressions for x = 12.
x
0
x
1
x
−1
EXAMPLES
Evaluate the expressions for x = 2.
x
x0
−1
x −4
EXAMPLES
Rewrite as equivalent expressions with negative
exponents.
1
y
1
x3
1
82
EXAMPLES
Evaluate the expressions.
⎛5⎞
⎜ ⎟
⎝2⎠
−1
⎛5⎞
⎜ ⎟
⎝6⎠
−2
⎛ 1⎞
⎜ ⎟
⎝4⎠
−2
PRACTICE
Rewrite as an equivalent with a positive exponent.
x −4
6 −2
Evaluate the expressions.
13
−1
10 −3
Rewrite as an equivalent with a negative exponent.
1
x2
1
95
Evaluate the expressions for y = 9.
y
−2
PRACTICE
Evaluate the expressions.
⎛7⎞
⎜ ⎟
⎝5⎠
−1
⎛ 1⎞
⎜ ⎟
⎝ 12 ⎠
−2
FINAL QUESTION
7
Evaluate the expression for x = .
9
x
0