Mathwords: Exponent Rules

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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 ≠ 0)

4. (a ≥ 0, m ≥ 0, n > 0)

Combining

1. multiplication: a^xa^y = a^{x + y}

2. division: (a ≠ 0)

3. powers: (a^x)^y = a^xy

Distributing (a ≥ 0, b ≥ 0)

1. (ab)^x = a^xb^x

2. (b ≠ 0)

Careful!!

1. (a + b)ⁿ ≠ aⁿ + bⁿ

2. (a – b)ⁿ ≠ aⁿ – bⁿ

See also

Root formulas, nth root