25.
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Eksāmens MATEMĀTIKĀ 12. KLASEI
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### Teorija

Pakāpes
$\begin{array}{l}{a}^{n}=\underset{⏟}{a\cdot a\cdot a\cdot ...\cdot a}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}n\phantom{\rule{0.147em}{0ex}}\mathit{reizes}\end{array}$, ja $a\ne 0$.

${a}^{1}=a,\phantom{\rule{0.147em}{0ex}}{a}^{0}=1$
Piemērs:
$\begin{array}{l}{4}^{3}=4\cdot 4\cdot 4=64\\ {\left(-3\right)}^{4}=\left(-3\right)\left(-3\right)\left(-3\right)\left(-3\right)=81\end{array}$

Ja negatīva skaitļa kāpinātājs ir pāra skaitlis, tad skaitļa pakāpe ir pozitīvs skaitlis.
Ja negatīva skaitļa kāpinātājs ir nepāra skaitlis, tad pakāpe ir negatīvs skaitlis.
Piemērs:
${\left(-2\right)}^{4}=16;\phantom{\rule{1.029em}{0ex}}{\left(-2\right)}^{3}=-8$
Kāpināšanas īpašības
$\begin{array}{l}{a}^{m}\cdot {a}^{n}={a}^{m+n}\phantom{\rule{1.911em}{0ex}}{a}^{m}\cdot {b}^{m}={\left(\mathit{ab}\right)}^{m}\\ \\ {a}^{m}:{a}^{n}={a}^{m-n}\phantom{\rule{2.058em}{0ex}}\frac{{a}^{n}}{{b}^{n}}={\left(\frac{a}{b}\right)}^{n}\\ {\left({a}^{m}\right)}^{n}={a}^{\mathit{mn}}\end{array}$
Piemērs:
$\begin{array}{l}1\right)\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}{x}^{3}\cdot {x}^{6}={x}^{3+6}\phantom{\rule{0.147em}{0ex}}={x}^{9}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}2\right)\phantom{\rule{0.147em}{0ex}}{2}^{3}\cdot {5}^{3}={10}^{3}=1000\\ \\ 3\right)\frac{{3}^{8}}{{3}^{6}}={3}^{8}:{3}^{6}={3}^{8-6}={3}^{2}=9\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.588em}{0ex}}4\right)\phantom{\rule{0.147em}{0ex}}\frac{{8}^{6}}{{4}^{6}}={\left(\frac{8}{4}\right)}^{6}={2}^{6}=64\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\\ \\ 5\right)\phantom{\rule{0.147em}{0ex}}{\left({y}^{3}\right)}^{4}={y}^{3\cdot 4}={y}^{12}\end{array}$