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2-7 Powers and Exponents

Defintion exponent base The number times the base is multiplied. The number of bases there are. The number being used as a factor. The number being multiplied over and over again.

base The number being used as a factor. 5 x 5 x 5 Base

exponent The number times the base is multiplied. Exponent

Defintion power a number expressed using an exponent.

power a number expressed using an exponent. Power

Ch. 2-7 Powers and Exponents Recall the order of Operations: -An exponent tells how many times a number, or base, is used as a factor. Example: 23 = 2 * 2 * 2 where 2 is the base and 3 is the exponent -An expression using a base and an exponent is a power. Example: 42 is a power Example 1: Write the following expressions using exponents. a.) 2 * 2 * 5 * 5 * 5 * 5 b.) a * a * a * a * b * b * b 22 * 54 a4 * b3 Recall the order of Operations: 1.) Work inside grouping symbols 2.) Simplify Powers (exponents) 3.) Multiply and divide from left to right whatever comes first 4.)Add and subtract from left to right whatever comes first

Example 1: Simplify the following powers below. a.)(-5)4 b.) -52 c.) (-2)3 625 -25 -8 *Make sure that if the negative sign is in the parentheses you include it when you multiply that number by itself however many times. *If it is not inside parentheses then your answer is ALWAYS negative! Example 2: Simplify each expression below. a.) 26 – (2 * 5)2 b.) -4 + 6 * 32 Simplify parentheses first 26 – (10)2 Simplify the power first -4 + 6 * 9 Now simplify multiplication and then add -4 + 54 = 50 Now simplify the power 26 – 100 = -74

c.) (-3)2 + 12 * 2 d.) -22 + 6 * 1 Simplify the power first 9 + 12 * 2 Simplify the power first -4 + 6 * 1 Now simplify the multiplication and then add -4 + 6 = 2 Now simplify the multiplication and then add 9 + 24 = 33

26-38 show order of operation steps Homework Pg 88 #12-38 (skip 32) evens only 26-38 show order of operation steps #12-16 –> 2x2y3 Alpha order and not multiplication sign