Look for a Pattern in
Integer Exponents
Warm Up
Evaluate.
2. 100
1000
1
3. 102 • 102
10,000
1. 103
7
10
4.
104
6
10
5.
106
1000
1
Learn to evaluate expressions with
negative exponents.
10 2
10 • 10
100
÷10
101
100
10
1
10
1
÷10
–2
10–1
10
1
10 • 10
1
10
1 = 0.1 1 = 0.01
100
10
÷10
÷10
Look for a pattern in the table to extend what you know
about exponents to include negative exponents. Start
with what you know about positive and zero exponents.
Example: Using a Pattern to Evaluate
Negative Exponents
Evaluate the powers of 10.
A. 10–2
10–2
1
=
10 • 10
10–2
1
= 0.01
=
100
B. 10–1
10
–1
10 –1
1
=
10
= 1
10
= 0.1
Example: Using a Pattern to Evaluate
Negative Exponents Continued
Evaluate the powers of 10.
C. 10–6
10–6 =
10–6
1
10 • 10 • 10 • 10 • 10 • 10
1
=
= 0.000001
1,000,000
Try This
Evaluate the powers of 10.
A. 10–8
10–8 =
10–8
B. 10–9
1
=
= 0.00000001
100,000,000
1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
1
=
= 0.000000001
1,000,000,000
10–9 =
10–9
1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
Try This
Evaluate the powers of 10.
C. 10–7
1
10 • 10 • 10 • 10 • 10 • 10 • 10
10–7
=
10–7
1
=
= 0.0000001
10,000,000
NEGATIVE EXPONENTS
Words
Numbers
A power with a
negative exponent
1
1
–3
5
=
=
equals 1 divided by
53
125
that power with it’s
opposite exponent.
Algebra
b–n =
1
bn
Remember!
The reciprocal of a number is 1 divided by that
number.
Example: Evaluating Negative Exponents
Evaluate.
5–3
1
53
Write the reciprocal; change the
sign of the exponent.
1
5•5•5
1
125
Try This
Evaluate.
(–10)–3
1
–103
Write the reciprocal; change the
sign of the exponent.
1
(–10)(–10)(–10)
–
1
= –0.001
1000
Example: Evaluating Products and
Quotients of Negative Exponents
Evaluate.
A. 2–5 • 23
2–5+3 Bases are the same, so add the exponents.
2 –2
1
22
1
4
Write the reciprocal; change the sign of
the exponent.
3
1
2
3
Check: 2 •
=
5 • 2 =
2
25
1
2•2•2
=
=
2•2•2•2•2
4
–5
23
Example: Evaluating Products and
Quotients of Negative Exponents Continued
Evaluate.
B.
65
68
65–8
6 –3
1
63
Bases are the same, so
subtract the exponents.
Write the reciprocal; change
the sign of the exponent.
1
Check:
216
6 5=
68
1
6 •6 • 6 • 6 • 6
=
6 • 6 • 6 • 6 • 6 • 6 • 6 • 6 216
Try This
Evaluate.
52
A. 53
5 2–3
5 –1
Bases are the same, so subtract the
exponents.
1
51
Write the reciprocal; change the
sign of the exponent.
1
5
52 =
Check: 3
5
5•5
5 •5 • 5
= 1
5
Try This
Evaluate.
B. 7–6 • 77
Bases are the same, so add the
7–6+7
exponents.
1
7
7
7
1
–6
7
7 =
7
Check: 7 • 7 =
•
7
76
76
7•7•7•7•7•7•7
7
=
=
1
7•7•7•7•7•7
=7
Lesson Quiz: Part 1
Evaluate the powers of 10.
1. 10–3
0.001
2. 10–7
0.0000001
Evaluate.
3.
(–6)–2
4. 74 • 7–4
5. 92
95
1
36
1
1
729
Lesson Quiz: Part 2
6. In engineering notation, a tera is
equal to 1012, and a mega is
equal to 106. How many megas
are equal to a tera?
106