2. Exponents Chelsie Wright Exponents are a shorthand way to show how many times a number, called the base, is multiplied times itself.

3. Rule #1 They must have the same base To multiply powers of the same base, add the exponents! Example: a 2 a 3 = a 5

4. Solution The problem means: Multiply the numbers, then combine the powers of x : 3x 2 · 4x 5 · 2x = 24x 8 Two factors of x -- x 2 -- times five factors of x -- x 5 -- times one factor of x, produce a total of 2 + 5 + 1 = 8 factors of x : x 8.

5. Rule #2 Power of a product of factors Raise each factor to that same power! Example:(ab) 3 = a 3 b 3

6. Why do we do that? Again, according to what the symbols mean: (ab) 3 = ab· ab· ab = aaabbb = a 3 b 3. The order of the factors does not matter: ab· ab· ab = aaabbb.

7. Rule #3 Power of a power To take a power of a power, multiply the exponents! Example: (a 2 ) 3 = a 2· 3 = a 6

8. Why do we do that? Again, because of what the symbols mean: (a 2 ) 3 = a 2 a 2 a 2 = a 3· 2 = a 6 Again, because of what the symbols mean: (a 2 ) 3 = a 2 a 2 a 2 = a 3· 2 = a 6

9. Now you try some

10. Use Rule #1 to solve this problem 5x 2 · 6x 4 = a)a)30x 8 b)b)30x 6 c)c)30x 12

11. Nope! The correct answer is 30x6 You multiply the base and add the exponents.

12. CORRECT!

13. Nope! The correct answer is 30x6 You multiply the base and add the exponents.

14. Use Rule #2 to solve the problem (xy) 4 = a) a) xy 4 b) b) x 2 y 4 c) c) x 4 y 4

15. Nope! The correct answer is c)x 4 y 4

16. Nope! The correct answer is c)x 4 y 4

17. Correct!

18. Use Rule #3 to solve the problem (x 2 ) 5 = a)a)x 7 b)b)x 10 c)c)x 25

19. Nope! The correct answer is b)x10

20. Correct!

21. Nope! The correct answer is b)x10

22. Now that you know all three rules complete a few more practice problems

23. (a4)8 =(a4)8 = a)a)a 12 b)b)a 32 c)c)8a 4

24. Nope! The correct answer is b)a 32

25. Correct!

26. Nope! The correct answer is b)a 32

27. (3x 6 ) 2 = a)a)9x 12 b)b)6x 12 c)c)9x 36

28. Correct!

29. Nope! The correct answer is a)9x 12

30. Nope! The correct answer is a)9x 12

32. Works Cited "Decimals and Integers - Exponents - First Glance." Decimals and Integers - Exponents - First Glance. N.p., n.d. Web. 18 Feb. 2015. "Three Rules of Exponents." Three Rules of Exponents. N.p., n.d. Web. 17 Feb. 2015.