1. Powers & Exponents

2. Common Core Strand: 6.EE.1 Student Friendly Terms: Students will be able to simplify expressions containing positive and negative exponents, with 80% accuracy. Essential Question: How can I represent repeated multiplication in exponential form and vice versa?

3. Vocabulary:  Exponent – in a power, the number of times the base is used as a factor; in 10 3, the exponent is 3.  Base – in a power, the number used as a factor; in 10 3, the base is 10.  Power – a number written using exponents; powers represent repeated multiplication; the power 6 3 is read six to the third power, or seven cubed.  Squared – a number expressed to the second power.  Cubed – a number expressed to the third power. Powers & Exponents

4. Here Is Your Dilemma… - You have just won the grand prize in a lottery. The lottery commission tells you that you may choose from one of two cash prizes: Either - Option 1: $1,000 per day for 30 days - Option 2: $0.01 (one penny) the first day, $0.02 the next day, $0.04 the next day....for 30 days. Each day's pay is double the pay from the previous day. Which would you choose? Answer by entering the expressions in Maple below to represent amount of money for each at the end of 30 days. Powers & Exponents

5. Why would we need to know about powers and exponents? We need to understand powers and exponents because they can help solve day to day problems as well as help simplify more complex mathematical computations. Powers & Exponents

6. Real World Example Basketball Tournament Example 1: Your basketball team has just entered a tournament, and your team is told it will have to win 6 games to win the tournament (no team was given a bye). How many teams entered the tournament? Powers & Exponents

7. Real World Example Basketball Tournament Example 1: Your basketball team has just entered a tournament, and your team is told it will have to win 6 games to win the tournament (no team was given a bye). How many teams entered the tournament? Since you are playing 6 games and each game you play one team you know the number of teams is equal to two to the sixth power. 2 6 = 2 x 2 x 2 x 2 x 2 x 2 = 64 teams Powers & Exponents

8. Powers & Exponential Computation The expression 3 x 3 x 3 x 3 can be written as the power 3 4 and explained as follows: 3 4 Powers & Exponents A number expressed using an exponent is called a power The exponent tells how many times the base is used as a factor The base is the number that is being multiplied }

9. Powers & Exponential Table Powers & Exponents PowersWords Repeated Factors 2122232n2122232n2 2 to the first power 2 to the second power (squared) 2 to the third power (cubed) 2 to the nth power 22 · 22 · 2 · 22 · 2 ·…· 222 · 22 · 2 · 22 · 2 ·…· 2 · · ·

10. Write Powers & Products Example 1: Write 5 x 5 x 5 using exponents. Then find the value of the power. Powers & Exponents

11. Write Powers & Products Example 1: Write 5 x 5 x 5 using exponents. Then find the value of the power. 5 5 5 = 5 3 = 125 = 125 Powers & Exponents

12. Write Powers & Products Example 2: Write 4 5 as a product. Then find the value of the product. Powers & Exponents

13. Write Powers & Products Example 2: Write 4 5 as a product. Then find the value of the product. 4 5 = 4 4 4 4 4 4 5 = 4 4 4 4 4 = 16 4 4 4 = 16 4 4 4 = 64 16 = 64 16 = 1024 = 1024 Powers & Exponents

14. Write Powers & Products Example 3: Write a a b b a b using exponents. Powers & Exponents

15. Write Powers & Products Example 3: Write a a b b a b using exponents. a a b b a b = a a a b b b = (a a a) ( b b b) = (a a a) ( b b b) = a 3 b 3 = a 3 b 3 Powers & Exponents

16. Independent Practice Write each expression using exponents. 1) 2 2 2 2 2 2 2 2) 6 6 6 3) 2 2 2 2 4) 9 Powers & Exponents

17. Independent Practice Write each expression using exponents. 1) 2 2 2 2 2 2 2 = 2 7 2) 6 6 6 = 6 3 3) 2 2 2 2 = 2 4 4) 9 = 9 1 Powers & Exponents

18. Independent Practice Write each power as a product. 1) 2 6 2) 7 3 3) 8 2 4) nine cubed Powers & Exponents

19. Independent Practice Write each power as a product. 1) 2 6 = 2 2 2 2 2 2 2) 7 3 = 7 7 7 3) 8 2 = 8 8 4) nine cubed = 9 9 9 Powers & Exponents

20. We can also use powers and exponents to write prime factorizations of numbers Powers & Exponents

21. Homework Holt MS Math Textbook p.14 #26-40, even Powers & Exponents