Arithmetic Course/Number Operation/Power

Power

Power is a number of times a number multiply 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

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

$(-a)^-1 = -a^n$ . n=(2m+1)

Identities

$a^n + a^m = a^n (1 + a^(m-n))$
$a^n - a^m = a^n (1 - a^(m-n))$
$a^n \times a^m = a^(n+m)$
$\frac{a^n}{a^m} = a^(n-m)$
$(a^n)^m = a^(nm)$
$(\frac{a}{b})^n = \frac{a^n}{a^m}$

Reference

Exponential

Last modified on 1 May 2011, at 16:29