Powers
[[$ a^n = a \cdot a \cdot ... \cdot a $]] |
n factors, a = base number, n = exponent |
[[$ a^0 = 1 $]] |
[[$ a \neq 0$]], [[$0^0 $]] not defined |
[[$ a^{-p} = \dfrac{1}{a^p} $]] | [[$ a \neq 0 $]] |
[[$ \left( \dfrac{a}{b} \right)^{-p} = \left( \dfrac{b}{a}\right)^{p} $]] | [[$ a \neq 0 $]] |
Calculation rules
[[$ a^ma^n = a^{m+n} $]] | product of powers with the same base number |
[[$ \dfrac{a^m}{a^n} = a^{m-n} $]] | quotient of powers with the same base number |
[[$ (ab)^n = a^nb^n $]] | power of products |
[[$ \left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}$]] | power of a quotient |
[[$ (a^m)^n = a^{mn} = (a^n)^m $]] | power of a power |