Topic 7: Rules of Exponents
    Teaching Guide
    Mathematical Goals
    •
    Write and simplify expressions with rational numbers and exponents
    At a Glance
    The process for finding powers of rational numbers is the same as the
    process for finding powers of whole numbers. In Topic 7, students will
    practice writing expressions involving repeated multiplication using
    exponents. Students will simplify both decimals and fractions raised to
    powers. Students will also explore the rules of exponents.
    After Example 7.1, have students find the value of fractions raised to a
    power by finding the products of the fractions. Show that raising the
    numerators and denominators to the power gives the same result.
    Summarize the example by asking:
    •
    How can you write repeated products of two different numbers, such as
    1.2
    3
    1.2
    3
    1.2
    3
    7.5
    3
    7.5, using exponents?
    •
    What is another way to write
    ?
    •
    What is another way to write
    ?
    Homework Check
    When reviewing Exercise 10, ask:
    •
    What is the value of 1 raised to any power?
    •
    For a base that is greater than 1, does the value of a power increase or
    decrease as the exponent increases?
    •
    For a base that is less than 1 but greater than 0, does the value of a power
    increase or decrease as the exponent increases?
    Before Example 7.2, explain to students that an expression with a base
    and an exponent, such as 2
    5
    , is called a power. An expression like 2
    5
    ? 2
    6
    is a
    product of two powers. And expression like (2
    5
    )
    6
    is a power raised to a power.
    Summarize the example by asking:
    •
    Can you use the rule for multiplying two powers to simplify the
    expression
    ?
    •
    Can you use the rule for multiplying two powers to simplify the
    expression
    4
    2
    3 5
    2
    ?
    Before assigning Exercise 7, show students how to cancel common factors
    in the numerator and denominator of a fraction. Students may find it helpful
    to cross out common factors and write a 1 in the factor’s place. Remind
    students that they must cancel the same number of common factors in the
    numerator as they do in the denominator.
    Q
    1
    2
    R
    5
    3 Q
    1
    2
    R
    8
    Q
    1
    2
    R
    4
    3 Q
    1
    2
    R
    2
    Q
    1
    2
    R
    4
    3
    1
    2
    PACING
    2 days
    Assignment Guide for Topic 7
    Core
    Example 7.1 1–9, Example 7.2 1–6
    Advanced
    Example 7.1 10, Example 7.2 7–10
    Answers to Topic 7
    Exercises for Example 7.1
    1.
    (3.6)
    4
    2.
    3.
    (0.8)
    5
    4.
    5.
    12.96
    6.
    0.064
    7.
    113.44725
    8.
    9.
    or 0.0036
    10. a.
    0.1
    b.
    0.01
    c.
    0.001
    d.
    0.0001
    e.
    Answers may vary. Sample: The 1 is the
    same number of decimal places to the right
    of the decimal point as the exponent.
    f.
    0.00000001
    Exercises for Example 7.2
    1.
    7
    15
    2.
    3
    42
    3.
    235
    178
    4.
    17
    80
    5
    .5
    28
    6.
    2
    40
    7. a.
    b.
    c.
    9
    2
    d.
    = 9
    (5–3)
    = 9
    2
    e.
    To divide two numbers with the same base,
    subtract the exponents.
    f.
    11
    7
    8.
    x
    12
    9.
    m
    7
    10.
    p
    24
    9
    5
    9
    3
    9 3 9
    1
    9 3 9 3 9 3 9 3 9
    9 3 9 3 9
    9
    2500
    4
    1125
    1
    243
    Q
    4
    9
    R
    3
    Homework Check
    When reviewing Exercise 7, ask:
    •
    Can you use the rule for dividing two powers to simplify the expression
    ?
    •
    Can you use the rule for dividing two powers to simplify the expression
    5
    9
    ?
    6
    9
    0.25
    8
    0.25
    4

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