Exponent

Written by Jerry Ratzlaff. Posted in Mathematics

Repeated multiplication of the same base by itself.

  • \( a \times a \times a \times \ldots \times a = a^n \)
  • "a" is base, "n" is exponent

 

Product with base

  • \( a^n \times a^m = a^{n+m} \)

Product with exponent

  • \( a^n \times b^n = \left(a \times b \right)^n \)

Quotient with base

  • \( a^n\; / \; a^m = a^{n-m} \)

Quotient with exponent

  • \( a^n \; / \; b^n = \left( a \; /  \; b \right)^n \)

Power rule I

  • \( \left( a^n \right)^m = a^{n \cdot m} \)

Power rule II

  • \( a^{n^{m}} = a^\left( n^m \right) \)

Power with radicals

  • \( ^m  \sqrt { a^n } = a^ {n / m} \)

Negative exponents

  • \( a^{-n} = 1 \; / \; a^n  \)