Um die Aufgabe zu lösen, wende die Potenzgesetze an.

$9^{31}:9^{29}=9^{(31-29)}=9^2=819^\{31\}:9^\{29\}=\backslash \; 9^\{(31-29)\}\backslash \; =\backslash \; 9^2\backslash \; =\backslash \; 81$

$3^{-4}={\displaystyle \frac{1}{3^4}}3^\{-4\}\backslash \; =\backslash \; \backslash dfrac\{1\}\{\{3\}^4\}\backslash quad$Beachte die Potenzgesetze !

Jetzt kannst Du die Aufgabe fertig rechnen.

${\displaystyle \frac{1}{3^4}=\frac{1}{3\cdot 3\cdot 3\cdot 3}=\frac{1}{81}}\backslash displaystyle\backslash frac\{1\}\{3^4\}\backslash \; =\backslash \; \backslash frac\{1\}\{3\backslash cdot\; 3\backslash cdot3\backslash cdot3\}\backslash \; =\backslash \; \backslash frac\{1\}\{81\}$

$3^{-4}={\displaystyle \frac{1}{81}}3^\{-4\}\backslash \; =\backslash \; \backslash dfrac\{1\}\{81\}$