Ridicarea la putere a fractiilor ordinare

A ridica o fracție la o putere înseamnă a ridica numărătorul și numitorul la acea putere.

$$\begin{gathered} {\left(\frac{a}{b}\right)}^n=\underbrace{\frac{a}{b}·\frac{a}{b}·....·\frac{a}{b}}=\frac{a^n}{b^n}, a, b\in \mathrm{\mathbb{N}}, b\ne 0, n\in {\mathrm{\mathbb{N}}}^{*} \\ n ori \end{gathered}$$

Reguli de calcul cu puteri

${\left(\frac{a}{b}\right)}^m·{\left(\frac{a}{b}\right)}^n={\left(\frac{a}{b}\right)}^{m+n}, a, b\in {\mathrm{\mathbb{N}}}^{*}, m, n\in \mathrm{\mathbb{N}}$

${\left(\frac{a}{b}\right)}^m:{\left(\frac{a}{b}\right)}^n={\left(\frac{a}{b}\right)}^{m-n}, a, b\in {\mathrm{\mathbb{N}}}^{*}, m, n\in \mathrm{\mathbb{N}}, m\ge n$

${\left[{\left(\frac{a}{b}\right)}^m\right]}^n={\left(\frac{a}{b}\right)}^{m·n}, a, b\in {\mathrm{\mathbb{N}}}^{*}, m, n\in \mathrm{\mathbb{N}}$

${\left(\frac{a}{b}\right)}^n·{\left(\frac{c}{d}\right)}^n={\left(\frac{a}{b}·\frac{c}{d}\right)}^n, a, b, c, d\in {\mathrm{\mathbb{N}}}^{*}, n\in \mathrm{\mathbb{N}}$

${\left(\frac{a}{b}\right)}^0=1, a, b\in {\mathrm{\mathbb{N}}}^{*}$

${\left(\frac{a}{b}\right)}^1=\frac{a}{b}, a, b\in \mathrm{\mathbb{N}}, b\ne 0.$