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