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Properties of Exponents

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Title: Section 4.2 Division with Exponents Author: Walter Cotter Last modified by: jeffrey Created Date: 10/18/2002 3:38:41 PM Document presentation format – PowerPoint PPT presentation

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Title: Properties of Exponents


1
Properties of 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
By the Definition of Exponents
Notice that 5 3 2
17
Examples
18
Negative Exponents
Notice that 3 5 -2
19
Definition of Negative Exponents
  • If r is a positive integer, then

20
Examples of Negative Exponents
Notice that Negative Exponents do not indicate
negative numbers.
Negative exponents do indicate Reciprocals.
21
Examples of Negative Exponents
Notice that exponent does not touch the 3.
22
Property 4 for Exponents
  • If a is any real number and r and s are integers,
    then

To divide like bases subtract the exponents.
23
Property 5 for Exponents
  • If a and b are any two real numbers and r is an
    integer, then

The power of a quotient is the quotient of the
powers.
24
Property 5 Example
The power of a quotient is the quotient of the
powers.
25
Zero as an Exponent
26
Zero to the Zero?
Undefined
STOP
Zeros are not allowed in the denominator. So 00
is undefined.
27
Examples
28
Exponent Rules Summary
Properties
Definitions
29
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.

30
Write 1349.7 in scientific notation.
3
31
Write 1.85 x 104 in expanded notation.
4
32
More on Scientific Notation
How far does the decimal point move?
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