Warm Up Lesson Presentation Lesson Quiz - Warm Up Lesson Presentation Lesson Quiz. Holt Algebra 1 1-4

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  • Holt Algebra 1

    1-4 Powers and Exponents1-4 Powers and Exponents

    Holt Algebra 1

    Warm Up

    Lesson Presentation

    Lesson Quiz

  • Holt Algebra 1

    1-4 Powers and Exponents

    Warm Up

    Simplify.

    1. 2(2)

    2. (–2)(–2)

    3. (–2)(–2)(–2)

    4. 3(3)(3)

    4

    4

    –8

    27

    4 9

    5.

  • Holt Algebra 1

    1-4 Powers and Exponents

    Evaluate expressions containing exponents.

    Objective

  • Holt Algebra 1

    1-4 Powers and Exponents

    power

    base

    exponent

    Vocabulary

  • Holt Algebra 1

    1-4 Powers and Exponents

    A power is an expression written with an exponent and a base or the value of such an expression. 3² is an example of a power.

    The base is the

    number that is used as a factor.

    32 The exponent, 2 tells

    how many times the base, 3, is used as a factor.

  • Holt Algebra 1

    1-4 Powers and Exponents

    When a number is raised to the second power, we usually say it is “squared.” The area of a square is s  s = s2, is the side length.

    S

    S

    When a number is raised to the third power, we usually say its “cubed.” The of volume of a cube is s  s  s = s3 is the side length.

    S

    S S

  • Holt Algebra 1

    1-4 Powers and Exponents

    Write the power represented by the geometric model.

    5 5

    5 The figure is 5 units long, 5 units wide, and 5 units tall. 5  5  5

    The factor 5 is used 3 times.53

    Example 1A: Writing Powers for Geometric Models

  • Holt Algebra 1

    1-4 Powers and Exponents

    Write the power represented by the geometric model.

    The figure is 6 units long and 6 units wide. 6 x 6

    The factor 6 is used 2 times.62

    6

    6

    Example 1B: Writing Powers for Geometric Models

  • Holt Algebra 1

    1-4 Powers and Exponents

    Write the power represented by each geometric model.

    a.

    22

    b.

    Check It Out! Example 1

    x

    x

    x

    The figure is 2 units long and 2 units wide. 2  2

    The factor 2 is used 2 times.

    The figure is x units long, x units wide, and x units tall. x  x  x

    The factor x is used 3 times.x3

  • Holt Algebra 1

    1-4 Powers and Exponents

    There are no easy geometric models for numbers raised to exponents greater than 3, but you can still write them using repeated multiplication or a base and exponent.

    3 to the second power, or 3 squared

    3  3  3  3  3

    Multiplication Power ValueWords

    3  3  3  3

    3  3  3

    3  3

    33 to the first power

    3 to the third power, or 3 cubed

    3 to the fourth power

    3 to the fifth power

    3

    9

    27

    81

    243

    31

    Reading Exponents

    32

    33

    34

    35

  • Holt Algebra 1

    1-4 Powers and Exponents

    Caution! In the expression –52, 5 is the base because the negative sign is not in parentheses. In the expression (–2), –2 is the base because of the parentheses.

  • Holt Algebra 1

    1-4 Powers and Exponents

    Evaluate each expression.

    A. (–6)3

    (–6)(–6)(–6)

    –216

    B. –102

    –1 • 10 • 10

    –100

    Use –6 as a factor 3 times.

    Find the product of –1 and

    two 10’s.

    Example 2: Evaluating Powers

    Think of a negative sign in front of a power as multiplying by a –1.

  • Holt Algebra 1

    1-4 Powers and Exponents

    Use as a factor 2 times.2 9

    Evaluate the expression.

    C.

    2 9

     2 9

    Example 2: Evaluating Powers

    = 4

    81 2 9

     2 9

  • Holt Algebra 1

    1-4 Powers and Exponents

    Evaluate each expression.

    a. (–5)3

    b. –62

    Check It Out! Example 2

    (–5)(–5)(–5) Use –5 as a factor 3 times.

    –125

    –1  6  6

    –36

    Think of a negative sign in front of a power as multiplying by –1.

    Find the product of –1 and two 6’s.

  • Holt Algebra 1

    1-4 Powers and Exponents

    Check It Out! Example 2

    Evaluate the expression.

    c.

    Use as a factor 3 times.3 4

    27 64

  • Holt Algebra 1

    1-4 Powers and Exponents

    Write each number as a power of the given base.

    A. 64; base 8

    8  8

    82

    B. 81; base –3

    (–3)(–3)(–3)(–3)

    (–3)4

    The product of two 8’s is 64.

    The product of four –3’s is 81.

    Example 3: Writing Powers

  • Holt Algebra 1

    1-4 Powers and Exponents

    Write each number as a power of a given base.

    a. 64; base 4

    b. –27; base –3

    Check It Out! Example 3

    4  4  4 The product of three 4’s is 64.

    43

    (–3)(–3)(–3)

    –33

    The product of three (–3)’s is –27.

  • Holt Algebra 1

    1-4 Powers and Exponents

    In case of a school closing, the PTA president calls 3 families. Each of these families calls 3 other families and so on. How many families will have been called in the 4th round of calls?

    The answer will be the number of families contacted in the 4th round of calls.

    Example 4: Problem-Solving Application

    Understand the problem1

    List the important information:

    • The PTA president calls 3 families.

    • Each family then calls 3 more families.

  • Holt Algebra 1

    1-4 Powers and Exponents

    Draw a diagram to show the number of

    Families called in each round of calls.

    2 Make a Plan

    Example 4 Continued

    2nd round of calls

    1st round of calls

    PTA President

  • Holt Algebra 1

    1-4 Powers and Exponents

    Notice that after each round of calls the number of families contacted is a power of 3.

    1st round of calls: 1  3 = 3 or 31 families contacted

    So, in the 4th round of calls, 34 families will have

    been contacted.

    34 = 3  3  3  3 = 81 Multiply four 3’s.

    In the fourth round of calls, 81 families will have been contacted.

    2nd round of calls: 3  3 = 9 or 32 families contacted

    3rd round of calls: 9  3 = 27 or 33 families contacted

    Solve3

    Example 4 Continued

  • Holt Algebra 1

    1-4 Powers and Exponents

    Drawing a diagram helps you visualize the

    problem, but the numbers become too large for a diagram. The diagram helps you recognize the pattern of multiplying by 3 so that you can write the number as a power of 3.

    Look Back4

    Example 4 Continued

  • Holt Algebra 1

    1-4 Powers and Exponents

    What if…? How many bacteria will be on the slide after 8 hours?

    Check it Out! Example 4

    28 After each hour, the number of bacteria is a power of 2.

    2  2  2  2  2  2  2  2 Multiply eight 2’s.

    The product of eight 2’s.256

  • Holt Algebra 1

    1-4 Powers and Exponents

    1. Write the power represented by the geometric model.

    n

    n n 2

    Simplify each expression.

    2.

    4. 6

    3. –63

    5. (–2)6

    −216

    216 64

    Lesson Quiz

    Write each number as a power of the given base.

    6. 343; base 7 7. 10,000; base 1073 104

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