1140 L2 - Lecture 2 Section A.2 Exponents and Radicals...

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Lecture 2: Section A.2 Exponents and Radicals Integer Exponents Def. If a is a real number and n is a positive integer, then a n = where a is the base and n is the exponent or power . ex. ( ± 3) 4 = ± 3 4 = ( ± 2) 3 = ± 2 3 = NOTE: 1) Zero exponent: If a 6 = 0, then a 0 = 2) Negative exponents: if a 6 = 0 and n is a positive integer, then a ± n =

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Properties of Exponents Let a and b be nonzero real numbers, variables, or algebraic expressions, and let m and n be integers. 1. a m a n = 2. a m a n = 3. ( ab ) m = 4. ( a m ) n = 5. ± a b ² m = 6. j a 2 j = j a j 2 = ( ± a ) 2 = a 2 NOTE: 1. ± a b ² ± m = 2. a ± m b ± n =
ex. Simplify the expression, writing answers without negative exponents. ± ab 3 ² ± 3 ³ ± a 2 b 2 ´ ± 4

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Radicals Def. A number b is said to be an n th root of a if a = b n . ex. 2 is a square root of 4 because the number ± 2 is also a square root of 4 because Def. Every real number a has exactly one n th root n p a when n is an odd integer. However, every positive real number has two n th root when n is an even integer and we use the symbol n p
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1140 L2 - Lecture 2 Section A.2 Exponents and Radicals...

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