Multiplication with Exponents

1
Section 4.1

• Multiplication with Exponents

2
Definition of Exponent

• An exponent is the power p in an expression ap.
• 52
• The number 5 is the base.
• The number 2 is the exponent.
• The exponent is an instruction that tells us how
  many times to use the base in a multiplication.

3
Examples

• 43
• -34
• (-2)5
• (-3/4)2

• (4)(4)(4) 64
• (-)(3)(3)(3)(3) -81
• (-2)(-2)(-2)(-2)(-2) -32
• (-3/4)(-3/4) (9/16)

4
Puzzler

• (-5)2 -52?
• (-5)(-5) -(5)(5)
• 25 -25

5
Multiplication with Exponents by Definition

• 32 35
• (3)(3) (3)(3)(3)(3)(3)
• 37
• Note 257

6
Property 1 for Exponents

• If a is any real number and r and s are integers,
  then

To multiply two expressions with the same base,
add exponents and use the common base.
7
Examples of Property 1
8
Examples of Property 1
9
Examples of Property 1
10
Power to a Power by Definition

• (32)3
• ((3)(3))1((3)(3))1((3)(3))1
• 36
• Note 3(2)6

11
Property 2 for Exponents

• If a is any real number and r and s are integers,
  then

A power raised to another power is the base
raised to the product of the powers.
12
Examples of Property 2
One base, two exponents multiply the exponents.
13
Property 3 for Exponents

• If a and b are any real number and r is an
  integer, then

Distribute the exponent.
14
Examples of Property 3
15
Examples of Property 3
16
Count

• How long is the edge?
• How many squares in the face?
• How many blocks?

1
1
1
17
Count
2
4
8
18
Count
2
4
8
3
9
27
19
Count
n
n2
n3
2
4
8
3
9
27
4
16
64
5
25
125
20
Suppose it is not a cubecount the blocks.
21
Suppose it is not a cubecount the blocks.
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Definition Scientific Notation

• A number is in scientific notation when it is
  written as the product of a number between 1 and
  10 and an integer power of 10.
• A number written in scientific notation has the
  form
• where 1lt n lt 10 and r an integer.

23
Write 1349.7 in scientific notation.
3
24
Write 1.85 x 104 in expanded notation.
4
25
Scientific Notation

• I once owned a truck with 176,000 miles on it.
• If I had put 10,000 more miles on it would have
  traveled the equivalent of one light second.
• Express a light second in miles using scientific
  notation.

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Getting Ready for Class

• Explain the difference between -52 and (-5)2.
• How do you multiply two expressions containing
  exponents when they have the same base?
• What is property 2 for exponents?
• When is a number written in scientific notation?

27
Homework 4.1

• Page 249
• 1-99 odd