Name: ___________________________________________
Date: ______________
4.6 – Negative and Zero Exponents
Consider the following pattern of powers of 2.
23 = 8
22 = 4
21 = 2
20 = ?
2-1 = ?
2-2 = ?
Negative and Zero Exponents
0
For any nonzero number a, a = 1.
-n
For any nonzero number a and any integer n, a
1
= an
Example 1 – Powers with Negative and Zero Exponents
Write the expression using only positive exponents.
a) 3-5
b) m0n-4
c) 16x-6y
Checkpoint!
Write the expression using only positive exponents.
a) 5-2
b) 1,000,0000
c) 3y-2
d) a-7b3
REWRITING FRACTIONS You can use the prime factorization of a number to write a
fraction as an expression involving negative exponents.
Example 2 – Rewriting Fractions
Write the expression without using a fraction bar.
a)
1
16
b)
a2
c3
Example 3 – Using Powers Properties with Negative Exponents
Find the product or quotient. Write your answer using only positive exponents.
a)
5 5
10
6
b)
8 n 3
n2
Checkpoint
Write the expression without using a fraction bar.
5.
1
25
6.
1
1000
7.
2
a8
8.
x7
z2
Find the product or quotient. Write your answer using only positive exponents.
9.
13.
37  311
2 3
24
10.
14.
5 8  5 7
72
7 8
11.
m 3  m 1
12.
a 2  a10
15.
5k 3
k 9
16.
b 4
b 6
Example 4 – Solving Problems Using Negative Exponents
GECKOS Geckos can easily climb smooth vertical surfaces. Biologists have discovered
that tiny hairs are the reason that the feet of a gecko are so sticky. Each hair is about
100 micrometers long. A micrometer is 10-6 meter. What is the length of one hair in
meters?