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