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1.3 (Powers and Exponents) DATE Vocabulary *** Expanded notation: a number expanded by place value. Ex: 325,706 = 300,000 + 20,000 + 5,000 + 700 + 6 *** Standard Form: written as a whole number. Ex: 325,706 *** Word Form: Three Hundred Twenty-five Thousand Seven Hundred Six *** Factor: Whole numbers other than 0 that are multiplied together to get the answer (product). Ex: 12 x 10 x 4 x 14 *** Power: Used to write a product that has a repeated factor. Ex: 10 x 10 x 10 x 10 = 104 *** Base: The number that is the repeated factor. *** Exponent: The number of times the factor is repeated Base Exponent (Power) 63 = 6 x 6 x 6 There are 3 factors *** Exponential Form: 63 *** Reading Powers: 32 is read “3 to the second power” or “3 squared.” Ex: 43 is read “4 to the third power” or “4 cubed.” 25 is read “2 to the fifth power.” Examples ** Ex. 1: Writing a Power 100,000 = 10 x10 x 10 x 10 x 10 = 105 There are 5 factors of 10 in 100,000 Try these on your own a. 8 x 8 x 8 = c. 20 x 20 = e. 7 x 7 x 7 x 7 x 7 = b. 6 x 6 x 6 x 6 = d. 11 x 11 x 11 x 11 x 11 = f. 15 x 15 x 15 = ** Ex. 2: Finding the value of a power a. Find the value of five cubed 53 = 5 x 5 x 5 = 125 Write 5 as a factor three times Multiply b. Find the value of two to the sixth power 26 = 2 x 2 x 2 x 2 x 2 x 2 Write 2 as a factor six times = 64 Multiply Try these on your own Write the products. Then find the value. a. 112 b. 54 c. 3 to the sixth power d. 6 squared ** Ex. 3: Powers in the Real-World Problems Listen to the following story problem and write an equation using powers and exponents and find the value. Review/Ticket out the Door