Du sollst folgenden Term berechnen: $-\mathrm{38,8}-\mathrm{14,4}\cdot 2-38\{,\}8-14\{,\}4\backslash cdot2$

Aufgrund der "Punkt vor Strich"-Regel berechne zuerst $\mathrm{14,4}\cdot 2=\mathrm{28,8}14\{,\}4\backslash cdot2=28\{,\}8$

Jetzt kannst Du die Aufgabe fertig rechnen.

$-\mathrm{38,8}-\mathrm{14,4}\cdot 2=-\mathrm{38,8}-(\mathrm{14,4}\cdot 2)=-\mathrm{38,8}-\mathrm{28,8}=-\mathrm{67,6}-38\{,\}8-14\{,\}4\backslash cdot2\backslash \backslash =-38\{,\}8-\backslash left(14\{,\}4\backslash cdot2\backslash right)\backslash \backslash =-38\{,\}8-28\{,\}8\backslash \backslash =-67\{,\}6$

Du sollst den folgenden Term berechnen: ${\left({\displaystyle \frac{1}{2}}\right)}^2\cdot 2^{-2}\backslash left(\backslash dfrac\{1\}\{2\}\backslash right)^\{2\}\backslash cdot2^\{-2\}$

Berechne zuerst die Potenzen.

${\left({\displaystyle \frac{1}{2}}\right)}^2={\displaystyle \frac{1}{4}}\backslash left(\backslash dfrac\{1\}\{2\}\backslash right)^\{2\}\; =\; \backslash dfrac\{1\}\{4\}$

$2^{-2}={\displaystyle \frac{1}{2^2}}={\displaystyle \frac{1}{4}}2^\{-2\}\; =\backslash dfrac\{1\}\{\{2\}^\{2\}\}\; =\; \backslash dfrac\{1\}\{4\}$ Beachte die Potenzgesetze !

Jetzt kannst Du die Aufgabe fertig rechnen.

${\left({\displaystyle \frac{1}{2}}\right)}^2\cdot 2^{-2}\backslash left(\backslash dfrac\{1\}\{2\}\backslash right)^\{2\}\backslash cdot2^\{-2\}$

$={\left({\displaystyle \frac{1}{2}}\right)}^2\cdot {\displaystyle \frac{1}{2^2}}=\backslash left(\backslash dfrac\{1\}\{2\}\backslash right)^\{2\}\backslash cdot\backslash dfrac\{1\}\{\{2\}^2\}$

$={\displaystyle \frac{1}{4}}\cdot {\displaystyle \frac{1}{4}}=\backslash dfrac\{1\}\{4\}\backslash cdot\backslash dfrac\{1\}\{4\}$

$={\displaystyle \frac{1}{16}}=\backslash dfrac\{1\}\{16\}$