Power

A power \(a^n\) is a product in which the base \(a\) appears as a factor \(n\) times:

\[ a^n = \underbrace{a \cdot a \cdot \ldots \cdot a}_{n} \]

• Rules. \(a^m \cdot a^n = a^{m+n}\), \(\frac{a^m}{a^n} = a^{m-n}\) and \((a^m)^n = a^{mn}\).
• Zero as the exponent. \(a^0 = 1\) when \(a \neq 0\).
• A negative base. Brackets make the difference: \((-2)^4 = 16\), but \(-2^4 = -16\).