2.  What are exponents?  Exponents are numbers that show how many times a base is used as a factor.  How do we use exponents?  Exponents will tell us how many times to multiply the base number.  4 3  exponent base

3. 2424  2 x 2 x 2 x 2  4 x 2 x 2  8 x 2  16 6363  6 x 6 x 6  36 x 6  216

4.  You’ve already learned how to use exponents to indicate repeated multiplication.  What happens when you multiply two powers with the same base?  Ex. 7 2 7 3

5.  Ex. 7 2 7 3  (7 7) (7 7 7) 7575  Notice that 7 2 7 3 = 7 5,  So, when you multiply powers with the same base, you can add the exponents. 7 2 7 3 = 7 2 + 3 = 7 5

6.  To multiply numbers or variables with the same base, add the exponents.  Arithmetic Algebra  2 3 2 4 a m a n  2 3 + 4 a m + n  2 7

7.  3 3 3  a 5 a b 2

8.  You can find the power of a power by using the rule for Multiplying Powers with the Same Base like in Part I.  (7 2 ) 3 =  (7 2 )(7 2 )(7 2 ) *Notice that you can raise  7 2 + 2 + 2 a power to a power by  7 6 multiplying the exponents  (7 2 ) 3 = 7 2 3 = 7 6

9.  Arithmetic  (2 3 ) 4  2 3 4  2 12  Algebra  (a m ) n  a m n

10.  (3 2 ) 3  (a 6 ) 2