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Simplifying Exponents

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Continued Simplify powers Flip Negative Exponents to make Positive Exponents Now make all of the exponents positive by looking at each factor and deciding if ... – PowerPoint PPT presentation

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Title: Simplifying Exponents


1
Simplifying Exponents
  • Algebra I

2
Contents
  • Multiplication Properties of Exponents .1 13
  • Zero Exponent and Negative Exponents14 24
  • Division Properties of Exponents .15 32
  • Simplifying Expressions using Multiplication and
    Division Properties of Exponents33 51
  • Scientific Notation ..52 - 61

3
Multiplication Properties of Exponents
  • Product of Powers Property
  • Power of a Power Property
  • Power of a Product Property

4
Product of Powers Property
  • To multiply powers that have the same base, you
    add the exponents.
  • Example

5
Practice Product of Powers Property
  • Try
  • Try

6
Answers To Practice Problems
  • Answer
  • Answer

7
Power of a Power Property
  • To find a power of a power, you multiply the
    exponents.
  • Example
  • Therefore,

8
Practice Using the Power of a Power Property
  1. Try
  2. Try

9
Answers to Practice Problems
  • Answer
  • Answer

10
Power of a Product Property
  • To find a power of a product, find the power of
    EACH factor and multiply.
  • Example

11
Practice Power of a Product Property
  • Try
  • Try

12
Answers to Practice Problems
  • Answer
  • Answer

13
Review Multiplication Properties of Exponents
  • Product of Powers PropertyTo multiply powers
    that have the same base, ADD the exponents.
  • Power of a Power PropertyTo find a power of a
    power, multiply the exponents.
  • Power of a Product PropertyTo find a power of a
    product, find the power of each factor and
    multiply.

14
Zero Exponents
  • Any number, besides zero, to the zero power is 1.
  • Example
  • Example

15
Negative Exponents
  • To make a negative exponent a positive exponent,
    write it as its reciprocal.
  • In other words, when faced with a negative
    exponentmake it happy by flipping it.

16
Negative Exponent Examples
  • Example of Negative Exponent in the Numerator
  • The negative exponent is in the numeratorto make
    it positive, I flipped it to the denominator.

17
Negative Exponents Example
  • Negative Exponent in the Denominator
  • The negative exponent is in the denominator, so I
    flipped it to the numerator to make the
    exponent positive.

18
Practice Making Negative Exponents Positive
  • Try
  • Try

19
Answers to Negative Exponents Practice
  • Answer
  • Answer

20
Rewrite the Expression with Positive Exponents
  • Example
  • Look at EACH factor and decide if the factor
    belongs in the numerator or denominator.
  • All three factors are in the numerator. The 2
    has a positive exponent, so it remains in the
    numerator, the x has a negative exponent, so we
    flip it to the denominator. The y has a
    negative exponent, so we flip it to the
    denominator.

21
Rewrite the Expression with Positive Exponents
  • Example
  • All the factors are in the numerator. Now look
    at each factor and decide if the exponent is
    positive or negative. If the exponent is
    negative, we will flip the factor to make the
    exponent positive.

22
Rewriting the Expression with Positive Exponents
  • Example
  • The 4 has a negative exponent so to make the
    exponent positiveflip it to the denominator.
  • The exponent of a is 1, and the exponent of b is
    3both positive exponents, so they will remain in
    the numerator.
  • The exponent of c is negative so we will flip c
    from the numerator to the denominator to make the
    exponent positive.

23
Practice Rewriting the Expressions with Positive
Exponents
  1. Try
  2. Try

24
Answers
  1. Answer
  2. Answer

25
Division Properties of Exponents
  • Quotient of Powers Property
  • Power of a Quotient Property

26
Quotient of Powers Property
  • To divide powers that have the same base,
    subtract the exponents.
  • Example

27
Practice Quotient of Powers Property
  • Try
  • Try

28
Answers
  • Answer
  • Answer

29
Power of a Quotient Property
  • To find a power of a quotient, find the power of
    the numerator and the power of the denominator
    and divide.
  • Example

30
Simplifying Expressions
  • Simplify

31
Simplifying Expressions
  • First use the Power of a Quotient Property along
    with the Power of a Power Property

32
Simplify Expressions
  • Now use the Quotient of Power Property

33
Simplify Expressions
  • Simplify

34
Steps to Simplifying Expressions
  1. Power of a Quotient Property along with Power of
    a Power Property to remove parenthesis
  2. Flip negative exponents to make them positive
    exponents
  3. Use Product of Powers Property
  4. Use the Quotient of Powers Property

35
Power of a Quotient Property and Power of a Power
Property
  • Use the power of a quotient property to remove
    parenthesis and since the expression has a power
    to a power, use the power of a power property.

36
Continued
  • Simplify powers

37
Flip Negative Exponents to make Positive
Exponents
  • Now make all of the exponents positive by looking
    at each factor and deciding if they belong in the
    numerator or denominator.

38
Product of Powers Property
  • Now use the product of powers property to
    simplify the variables.

39
Quotient of Powers Property
  • Now use the Quotient of Powers Property to
    simplify.

40
Simplify the Expression
  • Simplify

41
Step 1 Power of a Quotient Property and Power
of a Power Property
42
Step 2 Flip Negative Exponents
43
Step 3 Product of Powers Property
44
Step 4 Quotient of Powers Property
45
Simplifying Expressions
  • Given
  • Step 1 Power of a Quotient Property

46
Power of Quotient Property
  • Result after Step 1
  • Step 2 Flip Negative Exponents

47
Flip Negative Exponents
  • Step 3 Make one large Fraction by using the
    product of Powers Property

48
Make one Fraction by Using Product of Powers
Property
49
Use Quotient of Powers Property
50
Simplify the Expressions
  • Try
  • Try

51
Answers
  • Answer
  • Answer

52
Scientific Notation
  • Scientific Notation uses powers of ten to express
    decimal numbers.
  • For example
  • The positive exponent means that you move the
    decimal to the right 5 times.
  • So,

53
Scientific Notation
  • If the exponent of 10 is negative, you move the
    decimal to the left the amount of the exponent.
  • Example

54
Practice Scientific Notation
  • Write the number in decimal form
  • 1.
  • 2.

55
Answers
  • 1.
  • 2.

56
Write a Number in Scientific Notation
  • To write a number in scientific notation, move
    the decimal to make a number between 1 and 9.
    Multiply by 10 and write the exponent as the
    number of places you moved the decimal.
  • A positive exponent represents a number larger
    than 1 and a negative exponent represents a
    number smaller than 1.

57
Example of Writing a Number in Scientific Notation
  • Write 88,000,000 in scientific notation
  • First place the decimal to make a number between
    1 and 9.
  • Count the number of places you moved the decimal.
  • Write the number as a product of the decimal and
    10 with an exponent that represents the number of
    decimal places you moved.
  • Positive exponent represents a number larger than
    1.

58
Write 0.0422 in Scientific Notation
  • Move the decimal to make a number between 1 and 9
    between the 4 and 2
  • Write the number as a product of the number you
    made and 10 to a power 4.2 X 10
  • Now the exponent represents the number of places
    you moved the decimal, we moved the decimal 2
    times. Since the number is less than 1 the
    exponent is negative.

59
Operations with Scientific Notation
  • For example
  • Multiply 2.3 and 1.8 4.14
  • Use the product of powers property
  • Write in scientific notation

60
Try These
  • Write in scientific notation
  • 1.
  • 2.

61
Answers
  • 1.
  • 2.

62
The End
  • We have completed all the concepts of simplifying
    exponents. Now we just need to practice the
    concepts!
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