Rational Numbers & Equations

1. Lesson 14 Rational Numbers & Equations Powers and Exponents

2. Warm-Up • 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)

3. Powers and Exponents Target: 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

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 1 Write each expression as a power. (5)(5)(5)(5) • 54 (−11)(−11) • (−11)2 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 • 76

9. Example 2ab Write each power in expanded form and find its value. 82 • 8·8 = 64 (−1)5 • The exponent is odd so the answer will be negative. • (−1)(−1)(−1)(−1)(−1) = −1

10. Example 2c Write each power in expanded form and find its value. −44 • Read: “The opposite of four to the fourth power” • −(4)(4)(4)(4) = −256

11. Exit Problems Write each expression as a power. • 2∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 • (−1)(−1)(−1) Write each power in expanded form and find the value. • 23 • (−5)2 • (−3)3

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