Arithmetic Course/Number Operation/Power

Power

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

$a^n=\underset{n}{\underbrace{a\times \cdots \times a}},$

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