Arithmetic Course/Number Operation/Power

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Power[edit]

"Power" is the number of times a number is multiplied by itself

a^n = \underbrace{a \times \cdots \times a}_n,
a is raised to power of n is equal to a times a times a n times

Rules[edit]

  1. a^0 = 1
  2. a^1 = a
  3. a^-1 = \frac{1}{a}
  4. (-a)^-1 = a^n . n=2m
(-a)^-1 = -a^n . n=(2m+1)

Identities[edit]

  1. a^n + a^m = a^n (1 + a^(m-n))
  2. a^n - a^m = a^n (1 - a^(m-n))
  3. a^n \times a^m = a^(n+m)
  4. \frac{a^n}{a^m} = a^(n-m)
  5. (a^n)^m = a^(nm)
  6. (\frac{a}{b})^n = \frac{a^n}{a^m}