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# Exponents - Powers and Roots

## The laws of fractional and integer exponents.

### Integer Exponents

an am = an + m                             (1)

an / am = an - m                            (2)

(an)m = (am)n = an m                       (3)

(ab)m = am bm                          (4)

(a / b)m = am / bm                             (5)

p an ± q an = (p ± q) an                         (6)

a-n =  1 / an                               (7)

### Fractional Exponents

am/n = (am)1/n = (a1/n)m                        (8)

p (a)1/n ± q (a)1/n = (p ± q) a1/n                    (9)

(a b)1/n = a1/n b1/n                          (10)

a1/n / b1/n = (a / b)1/n                          (11)

(amx)1/nx = (am)1/n                          (12)

(-a)1/2 = i a1/2                            (13)

where

i = imaginary number

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## Citation

• The Engineering ToolBox (2008). Exponents - Powers and Roots. [online] Available at: https://www.engineeringtoolbox.com/exponents-d_1245.html [Accessed Day Month Year].

Modify the access date according your visit.

7.25.9

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