# Exponent rules

### What is an exponent

The base a raised to the power of n is equal to the multiplication of a, n times:

a n = × a × … × a

n times

a is the base and n is the exponent.

#### Examples

31 = 3

32 = 3 × 3 = 9

33 = 3 × 3 × 3 = 27

34 = 3 × 3 × 3 × 3 = 81

35 = 3 × 3 × 3 × 3 × 3 = 243

### Exponents rules and properties

 Product rules a n ? a m = a n+m 23 ? 24 = 23+4 = 128 a n ? b n = (a ? b) n 32 ? 42 = (3?4)2 = 144 Quotient rules a n / a m = a n–m 25 / 23 = 25-3 = 4 a n / b n = (a / b) n 43 / 23 = (4/2)3 = 8 Power rules (bn)m = bn?m (23)2 = 23?2 = 64 bnm = b(nm) 232 = 2(32)= 512 m?(bn) = b n/m 2?(26) = 26/2 = 8 b1/n = n?b 81/3 = 3?8 = 2 Negative exponents b-n = 1 / bn 2-3 = 1/23 = 0.125 Zero rules b0 = 1 50 = 1 0n = 0 , for n>0 05 = 0 One rules b1 = b 51 = 5 1n = 1 15 = 1 Minus one rule (-1)5 = -1 Derivative rule (xn)‘ = n?x n-1 (x3)‘ = 3?x3-1 Integral rule ? xndx = xn+1/(n+1)+C ? x2dx = x2+1/(2+1)+C

B. A. Operations Research & Statistics, California State University, Long Beach, Teaching Assistant undergraduate Mathematics. B.S. Mathematics, California State University, Long Beach. Mathematics University of California, Irvine, Teaching Assistant undergraduate Mathematics. Completed course work for MS Degree with 4.0 GPA. M.S. Mathematics, Kingsbridge University. Transcript available upon request. 1988-Present: Mathematics tutoring--One on one tutoring for SES students through YP institute and Academic advantage. Tutored students with low learning skills as well as very bright students. Tutored groups of four students in math classes from basic mathematics through calculus. Mathematics teaching for EFN, Inc., a private school.

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