Definition of a power

Raising to a power is an operation that appears continually in mathematics: it is the compact way of writing a repeated multiplication.

Definition — Power

Given $a\in\mathbb{R}$ (base) and $n\in\mathbb{N}$, with $n\ge 1$ (exponent): $a^n = \underbrace{a \cdot a \cdot \ldots \cdot a}_{n \text{ volte}}, \qquad a^0 = 1 \;\;(a\neq 0), \qquad a^{-n} = \frac{1}{a^n} \;\;(a\neq 0).$

The two extensions — exponent $0$ and negative exponent — are not arbitrary: they are chosen precisely so that the properties of powers continue to hold.

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Topics: Numbers and operations
Concepts: Power