Exponents - Powers and Roots

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Integer Exponents

aⁿ a^m = a^{n + m}         (1)

 aⁿ / a^m = a^{n - m}         (2)

(aⁿ)^m = (a^m)ⁿ = a^{n m}         (3)

(ab)^m = a^m b^m          (4)

(a / b)^m = a^m / b^m          (5)

p aⁿ ± q aⁿ = (p ± q) aⁿ   (6)

a^-n =  1 / aⁿ    (7)

Fractional Exponents

a^m/n = (a^m)^1/n = (a^1/n)^m         (8)

p (a)^1/n ± q (a)^1/n = (p ± q) a^1/n  (9)

(a b)^1/n = a^1/n b^1/n  (10)

a^1/n / b^1/n = (a / b)^1/n  (11)

(a^mx)^1/nx = (a^m)^1/n   (12)

(-a)^1/2 = i a^1/2   (13) where i = imaginary number

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