Algebra: Regneregler
Hva er potensregler?
Potensregler hjelper oss til å regne med tall som er opphøyd i noe, for eksempel:
$$a^x, \quad 10^x, \quad e^2$$Her er noen nyttige potensregler:
$$\begin{aligned} a^{\textcolor{red}{0}} &= 1 \\ a^{\textcolor{red}{1}} &= a \\ a^{\textcolor{red}{m}} \cdot a^{\textcolor{blue}{n}} &= a^{\textcolor{red}{m} + \textcolor{blue}{n}} \\ (a^{\textcolor{red}{m}})^{\textcolor{blue}{n}} & = a^{\textcolor{red}{m} \cdot \textcolor{blue}{n}} \\ (a\cdot b)^{\textcolor{red}{n}} & = a^{\textcolor{red}{n}} \cdot b^{\textcolor{red}{n}} \end{aligned}$$
$$\begin{aligned} a^{\textcolor{red}{-n}} & = \frac{1}{a^{\textcolor{red}{n}}} \\ \frac{a^{\textcolor{red}{n}}}{a^{\textcolor{blue}{m}}} & = a^{\textcolor{red}{n}-\textcolor{blue}{m}} \\ a^{1/\textcolor{red}{n}} & = \sqrt[\textcolor{red}{n}]{a} \end{aligned}$$
der $a \neq 0$.
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