Lesson 14 Rational Numbers Equations Powers and Exponents

Lesson 14 Rational Numbers & Equations Powers and Exponents

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

Powers and Exponents Target: Write and compute expressions with powers.

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

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

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.

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

Example 2 ab 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

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

Exit Problems Write each expression as a power. 1. 2∙ 2 ∙ 2 ∙ 2 2. (− 1)(− 1) Write each power in expanded form and find the value. 3. 4. 5. 23 (− 5)2 (− 3)3

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