Arithmetic Course/Number Operation/Power

Power

"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

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

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. $({\frac {a}{b}})^{n}={\frac {a^{n}}{a^{m}}}$