Exponent Law #3

Remember #1 and #2

In general:

1. Xa X Xb = Xa + b

In general:

2. Xa Xb = Xa - b

3. Power of PowersExpand the following:

Sometimes the base you are expanding is a power itself!

23 = 2 X 2 X 2

Expand the following:

Expand this in the same way

(22)3 22 X 22 X 22=

= 2 X 2 X 2 X 2 X 2 X 2 Which can be written as …

= 26

How many 2s are you multiplying?...

Examine the exponents

(22)3 = 26

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

(27)2=

1. 27 X 2 = 214

(43)4=

2. 43 X 4 = 412

(56)3=

3. 56 X 3 = 518

In General: EL #3

Let X be any baseLet a and b be any exponent

(Xa)b = X(ab)

Congratulations!!You have just

mastered the third exponent law

stop here

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