# Arithmetic Course/Number Operation/Power

## PowerEdit

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

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

## RulesEdit

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

## IdentitiesEdit

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