# Looking For a Pattern by ferda.gurcan

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```									       Look for Pattern
Look for a a Pattern in
4-2 inInteger Exponents
4-2 Integer Exponents

Warm Up
Problem of the Day
Lesson Presentation

Course
Course 3 3
Look for a Pattern
4-2       in Integer Exponents

Warm Up
Evaluate.
1. 103              1000
2. 100              1
3. 102 • 102         10,000

4. 107
1000
104
5.  106
1
106

Course 3
Look for a Pattern
4-2       in Integer Exponents

Problem of the Day
Find two different numbers for the values
of x and y that will make xy and yx equal.
2 and 4

Course 3
Look for a Pattern
4-2       in Integer Exponents

Learn to evaluate expressions with
negative exponents and to evaluate the
zero exponent.

Course 3
Look for a Pattern
4-2       in Integer Exponents

–2
10 2     101          100          10–1          10
10 • 10        10           1             1           1
10        10 • 10
1 = 0.1 1 = 0.01
100          10           1
10       100

÷ 10         ÷ 10         ÷ 10          ÷ 10

Look for a pattern in the table to extend what you
know about exponents to include negative exponents.

Course 3
Look for a Pattern
4-2       in Integer Exponents
Additional Example 1A & 1B: Using a Pattern to
Evaluate Negative Exponents
Evaluate the powers of 10.
A. 10–2
1          Extend the pattern
10–2   =
10 • 10       from the table.
1           Multiply. Write as a
10–2 =        = 0.01
100          decimal.
B. 10–1
1            Extend the pattern
10 –1 =                from the table.
10

10 –1 =   1    = 0.1   Multiply. Write as a
10           decimal.
Course 3
Look for a Pattern
4-2       in Integer Exponents
Check It Out: Example 1A

Evaluate the powers of 10.
10–8
Extend the pattern from the table.
1
10–8   =
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10

Multiply.
1
10–8   =
100,000,000
Write as a decimal.
= 0.00000001
Course 3
Look for a Pattern
4-2        in Integer Exponents
Check It Out: Example 1B

10–9
Extend the pattern from example 1A.
1
10–9       =
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
Multiply.
1
10–9   =
1,000,000,000
Write as a decimal.
= 0.000000001

Course 3
Look for a Pattern
4-2       in Integer Exponents

NEGATIVE EXPONENTS

Remember!
The reciprocal of a number is 1 divided by that
number.

Course 3
Look for a Pattern
4-2       in Integer Exponents
Exponents
Evaluate.
5–3
3   Write the reciprocal; change the
= 1
5           sign of the exponent.

=
1         Find the product of three 1 ’s.
5•5•5                                 5
1        Simplify.
=
125

Course 3
Look for a Pattern
4-2       in Integer Exponents
Exponents
Evaluate.
(–10)–3
1 3             Write the reciprocal; change
= –10              the sign of the exponent.

1                                       1 ’s.
=                  Find the product of three
–10 • –10 • –10                               –10

1
=       = –0.001   Simplify.
–1000

Course 3
Look for a Pattern
4-2       in Integer Exponents
Check It Out: Example 2A

Evaluate.
4–2
2       Write the reciprocal; change the
= 1
4              sign of the exponent.

=
1             Find the product of two 1 ’s.
4•4                                    4
1            Simplify.
=
16

Course 3
Look for a Pattern
4-2       in Integer Exponents
Check It Out: Example 2B

Evaluate.
(–7)–4
1    4            Write the reciprocal; change
=   –7                the sign of the exponent.

=
1              Find the product of four 1 ’s.
–7 • –7 • –7 • –7                              –7

1
=                      Simplify.
2401

Course 3
Look for a Pattern
4-2       in Integer Exponents

Course 3
Look for a Pattern
4-2       in Integer Exponents
Additional Example 3: Using the Order of Operations

Evaluate 5 – (6 – 4)–3 + (– 2)0.
5 – (6 – 4)–3 + (–2)0

= 5 – (2)–3 + (–2)0 Subtract inside the parentheses.

=5– 1+1                 Evaluate the exponents.
8

= 57                    Add and subtract from left to
8                    right.

Course 3
Look for a Pattern
4-2       in Integer Exponents
Check It Out: Example 3

Evaluate 3 + (7 – 4)–2 + (–8)0.
3 + (7 – 4)–2 + (–8)0

= 3 + (3)–2 + (–8)0 Subtract inside the parentheses.

=3+1 +1                 Evaluate the exponents.
9

9

Course 3
Look for a Pattern
4-2       in Integer Exponents
Lesson Quiz
Evaluate the powers of 10.

1. 10–3                     0.001

2. 10–7                    0.0000001

Evaluate.
1
3.     (–6)–2
36
3
4. 4 •       2–3   +   10–1   5
24
5.     80   – (11 –     24)–2     25
65
6.     (4w)–2   +   w–1   for w = 4 256
Course 3

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