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Dive into the third law of exponents with this comprehensive guide. Learn how to expand powers and manipulate exponents seamlessly. We'll cover essential properties such as (Xa)b = X(ab) and provide examples like expanding (22)3 and reducing powers to a single exponent. Gain confidence in identifying the base and exponents in various expressions while mastering the power of powers rule. This resource is ideal for students and anyone looking to strengthen their understanding of exponentiation in mathematics.
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Remember #1 and #2 In general: 1. XaX Xb = Xa + b In general: 2. XaXb = Xa - b
3. Power of Powers Expand the following: 23 = 2 X 2 X 2 Sometimes the base you are expanding is a power itself!
Expand the following: (22)3 22 X 22 X 22 = Expand this in the same way Which can be written as … = 2 X 2 X 2 X 2 X 2 X 2 How many 2s are you multiplying?... = 26
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 = 2. (43)4 43 X 4 = 412 = 3. (56)3 56 X3 = 518 =
In General: EL #3 Let X be any base Let a and b be any exponent (Xa)b = X(ab)
Congratulations!!You have just mastered the third exponent lawstop here
