1. Example 1
Using Zero and Negative Exponents a.
5 0
Definition of zero exponent 1 =
Definition of negative exponent =
5 4 1 b.
5 –4
625 1 =
Evaluate power. 2 1 –3 c. = 1 2 3
Definition of negative exponent

2. Example 1 1 = 1 8 = 8 Using Zero and Negative Exponents
Evaluate power. = 8 1 =
Divide. 8

3. A half-life is the amount of time that it takes for a
Example 2
Using Negative Exponents
SCIENCE
A half-life is the amount of time that it takes for a
radioactive substance to decay to one half of its
original quantity.
Suppose radioactive decay causes 400 grams of a
substance to decrease grams after 3 half-lives.
Evaluate to determine how many grams of
the substance are left.
400 
2 –3
400 
2 –3
SOLUTION 
400
2 –3 =
2 3 1
Definition of negative exponent

4. There are 50 grams left of the substance.
Example 2
Using Negative Exponents = 8 1
400
Evaluate exponent. = 50
Simplify.
ANSWER
There are 50 grams left of the substance.

5. Evaluate the expression.
Guided Practice
for Examples 1 and 2
Evaluate the expression.
ANSWER 49 1 1.
7 –2
ANSWER 32 1 – (
) –5 2 – 2. (
) 0 6 – 3.
ANSWER 1 4. 3 1 –2
ANSWER 9

6. In Example 2, suppose the substance has gone
Guided Practice
for Examples 1 and 2
WHAT IF?
In Example 2, suppose the substance has gone
through 4 half-lives. Evaluate to determine
how many grams are left. 
400
2 –4 5.
ANSWER
25 g
REASONING
Explain why the expression can be used to
find the amount of the substance in Example 2 that remains after n half-lives. 6. 
400
2 –n
ANSWER
2 –n
2 n 1 =
, which represents the number of
half-lives.