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Exponent Rules

Exponent Rules

Algebra rules and formulas for exponents are listed below.

 

Definitions

1. an = a·a·a···a  (n times)

2. a0 = 1  (a ≠ 0)

3. a to the power of negative n equals 1 divided by a to the power of n (a^-n = 1/a^n)  (a ≠ 0)

4. a^(m/n) = nth root of a^m, or (nth root of a)^m  (a ≥ 0, m ≥ 0, n > 0)

 

Combining

1. multiplication: axay = ax + y

2. division: Division rule for exponents: a^x divided by a^y equals a^(x-y), where a is not zero.  (a ≠ 0)

3. powers: (ax)y = axy

 

Distributing   (a ≥ 0, b ≥ 0)

1. (ab)x = axbx

2. Math formula showing exponent distribution over division: (a/b)^x = a^x / b^x  (b ≠ 0)

 

Careful!!

1. (a + b)n ≠ an + bn

2. (a – b)n ≠ an – bn

 

See also

Root formulas, nth root