Rekenregels machten

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Pas de correcte rekenregel(s) van machten toe [en reken uit indien mogelijk]

1. \((\frac{3}{7}b)^{-10}:(\frac{3}{7}b)^{-2}\)
2. \(-(-\frac{11}{3})^{-6}\)
3. \((-\frac{3}{13})^{-4}\)
4. \((\frac{7}{20}a)^{10}.(\frac{7}{20}a)^{-4}\)
5. \((\frac{16}{7})^{3}.(\frac{2}{3})^{3}\)
6. \((-17c^{10})^{-8}\)
7. \(-(-\frac{3}{5})^{-4}\)
8. \((-\frac{6}{5})^{-2}\)
9. \(-(-\frac{19}{6})^{-4}\)
10. \((\frac{6}{17}b)^{-7}:(\frac{6}{17}b)^{10}\)
11. \((-\frac{13}{7})^{-1}\)
12. \(-(-11)^{-4}\)

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Pas de correcte rekenregel(s) van machten toe [en reken uit indien mogelijk]

Verbetersleutel

1. \((\frac{3}{7}b)^{-10}:(\frac{3}{7}b)^{-2}=(\frac{3}{7}b)^{-10-(-2)}=(\frac{3}{7}b)^{-8}=(\frac{7}{3}\frac{1}{b})^{8}=\text{ZRM}\left[ =\frac{5764801}{6561} \frac{1}{b^{8}} \right]\)
2. \(-(-\frac{11}{3})^{-6}=-(-\frac{3}{11})^{6}=-\frac{3^{6}}{11^{6}}=\text{ZRM}\left[=-\frac{729}{1771561}\right]\)
3. \((-\frac{3}{13})^{-4}=(-\frac{13}{3})^{4}=+\frac{13^{4}}{3^{4}}=\text{ZRM}= \left[=\frac{28561}{81}\right]\)
4. \((\frac{7}{20}a)^{10}.(\frac{7}{20}a)^{-4}=(\frac{7}{20}a)^{10+(-4)}=(\frac{7}{20}a)^{6}\left[=\frac{117649}{64000000}a^{6}\right]=\text{ZRM}\)
5. \((\frac{16}{7})^{3}.(\frac{2}{3})^{3}=(\frac{16}{7}\frac{2}{3})^{3}=(\frac{32}{21})^{3}=\text{ZRM}=\left[\frac{32768}{9261}\right]\)
6. \((-17c^{10})^{-8}=(-17)^{-8}.(c^{10})^{-8}=(\frac{1}{-17})^{8}.(\frac{1}{c^{10}})^{8}=\text{ZRM}\left[=\frac{1}{6975757441} \frac{1}{c^{80}}\right]\)
7. \(-(-\frac{3}{5})^{-4}=-(-\frac{5}{3})^{4}=-\frac{5^{4}}{3^{4}}=\text{ZRM}\left[=-\frac{625}{81}\right]\)
8. \((-\frac{6}{5})^{-2}=(-\frac{5}{6})^{2}=+\frac{5^{2}}{6^{2}}= \left[=\frac{25}{36}\right]\)
9. \(-(-\frac{19}{6})^{-4}=-(-\frac{6}{19})^{4}=-\frac{6^{4}}{19^{4}}=\text{ZRM}\left[=-\frac{1296}{130321}\right]\)
10. \((\frac{6}{17}b)^{-7}:(\frac{6}{17}b)^{10}=(\frac{6}{17}b)^{-7-10}=(\frac{6}{17}b)^{-17}=(\frac{17}{6}\frac{1}{b})^{17}=\text{ZRM}\left[ =\frac{8.2724026188634E+20}{16926659444736} \frac{1}{b^{17}} \right]\)
11. \((-\frac{13}{7})^{-1}=(-\frac{7}{13})^{1}=-\frac{7^{1}}{13^{1}}= \left[=-\frac{7}{13}\right]\)
12. \(-(-11)^{-4}=-(-\frac{1}{11})^{4}=-\frac{1^{4}}{11^{4}}=\text{ZRM}\left[=-\frac{1}{14641}\right]\)