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Thursday 9/25

Thursday 9/25. Block 2 Integers In Class p.60 Lesson 2.6 Powers & Exponents Examples 1-2 Homework p.62 Exercises 1-27. Warm-Up. 1. List the following integers from least to greatest: −5, −11, 4, 8, −1, 0 2. Determine the SIGN of each answer. a. −209 + (− 184)

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Thursday 9/25

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  1. Thursday 9/25 • Block 2 Integers In Class p.60 Lesson 2.6 Powers & Exponents Examples 1-2 Homework p.62 Exercises 1-27

  2. Warm-Up 1. List the following integers from least to greatest: −5, −11, 4, 8, −1, 0 2. Determine the SIGN of each answer. a. −209 + (− 184) b. −88(45) c. −244 ÷ −8 d. 2065 − (−6310) −11, −5, −1, 0, 4, 8 – – + +

  3. Lesson 2.6 Powers and Exponents Write and compute expressions with powers.

  4. Vocabulary Power Used to express a product of a repeated factor. Powers consist of two parts, the base and the exponent. Base The repeated factor. Exponent Number of times the factor is repeated. Squared A number to the second power. Cubed A number to the third power.

  5. Powers, Bases and Exponents Exponent Repeated Factor Base Power Expanded Form

  6. Example 1 Write each expression as a power. a. (5)(5)(5)(5) 54 b. (−11)(−11) (−11)2 c. 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 76

  7. Power Rules for Positive and Negative Bases  If the base of a power is positive, the value of the power will always be positive.  If the base of a power is negative, the value of the power will be:  positive if the exponent is an even number.  negative if the exponent is an odd number.

  8. Example 2 Write each power in expanded form and find its value. a. 82Expanded form: 8  8 Value: 64 b. (−1)5Expanded form: (−1)(−1)(−1)(−1)(−1) The exponent is odd so the answer will be negative. Value: −1

  9. Example 2 Continued… Write each power in expanded form and find its value. c. −44 The expression −44 should be read “the opposite of four to the fourth power.” 44 = 256 so the opposite of 256 is −256 Value: −256

  10. Thursday 9/25 • Block 2 Integers In Class p.60 Lesson 2.6 Powers & Exponents Examples 1-2 Homework p.62 Exercises 1-27

  11. Exit Problems Write each expression as a power. 1. 2∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 2. (−1)(−1)(−1) 3. 23 4. (−5)2 5. (−3)3 26 (-1)3 Write each power in expanded form and find the value. (2)(2)(2) = 8 (–5)(–5) = 25 (–3)(–3)(–3) = –27

  12. Explore! Positive or Negative? Step 1 Copy the table below. Step 2 Fill in the table by writing each power in expanded form. Find the value of the power. The table has been started for you below.

  13. Explore! Positive or Negative? Step 3 Some of the answers are positive and some answers should be negative. Do you notice any patterns that would help you determine the sign of a power just by looking at the base and the exponent? Step 4 Use your pattern to determine the SIGN of each power. You do not need to find the value. a. 8⁵ b. (−9)⁴ c. (−6)¹¹ d. (−4)⁸ e. 12² f. (−1)¹⁷ Step 5 The expressions −3² and (−3)² are not equal. Explain why the two expressions are not equal and find the value of each expression.

  14. Communication Prompt How can you tell the sign of the value of a power without doing any computations?

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