# Exponents - Powers and Roots

### Integer Exponents

a^{n}a^{m}= a^{n + m}(1)

a^{n}/ a^{m}= a^{n - m}(2)

(a^{n})^{m}= (a^{m})^{n }= a^{n m}(3)

(ab)^{m}= a^{m}b^{m }(4)

(a / b)^{m}= a^{m }/ b^{m}(5)

p a^{n}± q a^{n}= (p ± q) a^{n}(6)

a^{-n}= 1 / a^{n}(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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