Exponent Law #3

Remember #1 and #2 In general: 1. X a X X b = X a + b In general: 2. X a X b = X a - b

3. Power of Powers Expand the following: Sometimes the base you are expanding is a power itself! 2 3 =2 X 2 X 2

Expand the following: Expand this in the same way (2 2 ) X 2 2 X 2 2 = = 2 X 2 X 2 X 2 X 2 X 2 Which can be written as … = 2 6 How many 2s are you multiplying?...

Examine the exponents (2 2 ) 3 = 2 6 What can you do with 2 and 3 to get 6? Multiply! Correct! This property is true for all power of powers with the same base.

Reduce the following to a single power (2 7 ) 2 = X 2 = 2 14 (4 3 ) 4 = X 4 = 4 12 (5 6 ) 3 = X 3 = 5 18

In General: EL #3 Let X be any base Let a and b be any exponent (X a ) b = X (ab)

Congratulations!! You have just mastered the third exponent law stop here

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