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Name:____________________ 8 CPP Chapter 7 Indices Rather than writing 2 2 2 , we can write such a product as 2 3 . This representation is called the index notation, where 2 is the base and 3 is the index or exponent. In general, for any positive integer n, a n = a a a a .......... . a n factors I- Index Laws: If m and n are any two positive integers, then: 1) a m a n = a m+n To ……………. powers having the same ………. but different …..., keep the ……….. and ………… the ………… am = a m−n , m n , a 0 n a To divide two powers having same ……… but different ……., where the ……… in the ……… is greater than that in the ….….., keep the base and subtract ………………. m a 1 3) n = n − m , m n , a 0 a a To divide two powers having same base different indices, where the …… in the numerator is …… than that in the denominator, keep the ……. and ………………. 2) 4) (a m ) n = a mn When raising a power to a ……., keep the …… and multiply the ……….. II- Expansion Laws: For a positive integer n, we have the following: 1) (ab) n = a n b n n an a 2) = n , b 0 . b b III- Zero Index Law: For all a 0 , a 0 = 1 . IV- V- Odd and Even Indices: • n If, then a 0 , a 0 • a n 0 if n is even a 0 , then: n a 0 if n is odd Negative Index Law: If a is any non-zero number and n is an integer, then a − n = Example: 2 −3 = 1 23 1 , thus a n and a − n are reciprocals. an