Exponentials and Logarithms Review

Exponentials and Logarithms Review - Exponentials and...

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11/5/2008 Exponentials and Logarithms Review Math 148 The Laws (or Rules) of Exponents 1. m n m n a a a + = 2. () m n m n a a = 3. 1 0 = a 4. n n a a 1 = 5. m n m n a a a = 6. ( ) n m mn m n a a a = = 7. kk k ab a b =⋅ 8. = m n a a n = m Comments 1. This rule is true for all positive numbers a . This just states that when you multiply the powers with the same base, the only thing you need to do to find the answer is to add the exponents. It also implies that you should not change anything in the base. 2. This is slightly different from what we have in 1. When we have a power of another power, we multiply the exponents. 3. This is a very important fact! 4. Negative exponents should not be taken to mean negative numbers. They just indicate repeated division! 5. No comment – See activities below 6. Calculations of higher degree roots and exponents have much in common. 7. When we have a product and we raise that product to a single power k , each factor must be raised separately to the one single power. This is true even when the bases a and b are different. 8. This is true if a follows all the restrictions, including 1 a . For all rules, we will assume that a and b are positive.
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Exponentials and Logarithms Review - Exponentials and...

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