Unit 7: Exponents and Exponential Functions
Day 2: Zero and Negative Exponents
Today we will...
Use patterns to help determine how to evaluate powers with a zero exponent
or negative exponent
Investigation
Use patterns to evaluate powers with zero or negative exponents.
1. Copy and complete the statements. Describe each pattern.
a) 25 = 32
24 = 16
23 =
22 =
21 =
20 =
b) 35 = 243
c)
105 =100 000
34 =
104 =
33 =
103 =
32 =
102 =
31 =
101 =
30 =
100 =
2.Reflect Express this as a general rule.
Any base raised to an exponent of zero equals
.
3. Continue your patterns from question 1 to evaluate the powers with negative
exponents. Express your answers as
whole numbers or fractions (no decimals).
0
2 =
30 =
100 =
2-1 =
3-1 =
10-1 =
2-2 =
3-2 =
10-2 =
2-3 =
3-3 =
10-3 =
4.Reflect Explain how to evaluate a power with a negative exponent.
Any base raised to a negative exponent is equal to the
base raised to a
of the
.
D1. Express as a power with a positive exponent.
1.) 7
-2
2.)
1
2−3
D2. Evaluate. Explain how the powers are different.
 
a) (-2)4
b) -24  
c) 2-4
Ex.) Write each as a single power with a positive exponent then
evaluate as whole number or a fraction (no decimals).
1.) 37x3-3
2.) 25÷2-3
3.) (53)-1
4.) 2-3 x 2-4
5.) 2-3÷2-5
6.) (2-2)-3