Write and compute expressions with powers. Powers & Exponents Write and compute expressions with powers.

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)

VOCAB 52 = 5 x 5 Factor: Base: Exponent: #’s multiplied together 2 x 3 = 6 factors Base: The repeated factor 5 x 5 x 5 x 5 x 5 x 5 5 is the repeated factor or BASE Exponent: Number of times the factor is repeated 6 Squared: A number to the 2nd power. 52 = 5 x 5 Cubed: 43 = 4 x 4 x 4

Powers, Bases and Exponents Repeated Factor Base Power Expanded Form

Power Rules for Positive and Negative Bases If the base is positive, the result will always be positive. If the base 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)(5)(5) 54 (−11)(−11) (−11)2 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 76

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

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

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

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