Rekenregels machten

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

1. \((-5)^{-6}\)
2. \((\frac{9}{4})^{-2}.(\frac{2}{3})^{-2}\)
3. \((2a)^{3}:(2a)^{-4}\)
4. \((-\frac{6}{19})^{-6}\)
5. \((\frac{12}{19}c)^{-10}.(\frac{12}{19}c)^{7}\)
6. \((15c^{8})^{-5}\)
7. \((\frac{8}{13})^{-1}.(\frac{14}{9})^{-1}\)
8. \((-\frac{6}{5})^{-4}\)
9. \((-3)^{-4}\)
10. \((-4)^{-3}\)
11. \((-\frac{8}{5})^{-1}\)
12. \((5c)^{6}.(5c)^{-9}\)

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

Verbetersleutel

1. \((-5)^{-6}=(-\frac{1}{5})^{6}=+\frac{1^{6}}{5^{6}}=\text{ZRM}= \left[=\frac{1}{15625}\right]\)
2. \((\frac{9}{4})^{-2}.(\frac{2}{3})^{-2}=(\frac{9}{4}\frac{2}{3})^{-2}=(\frac{3}{2})^{-2}=(\frac{2}{3})^{2}=\left[\frac{4}{9}\right]\)
3. \((2a)^{3}:(2a)^{-4}=(2a)^{3-(-4)}=(2a)^{7}=\text{ZRM}\left[ =128a^{7} \right]\)
4. \((-\frac{6}{19})^{-6}=(-\frac{19}{6})^{6}=+\frac{19^{6}}{6^{6}}=\text{ZRM}= \left[=\frac{47045881}{46656}\right]\)
5. \((\frac{12}{19}c)^{-10}.(\frac{12}{19}c)^{7}=(\frac{12}{19}c)^{-10+7}=(\frac{12}{19}c)^{-3}=(\frac{19}{12}\frac{1}{c})^{3}\left[=\frac{6859}{1728} \frac{1}{c^{3}}\right]=\text{ZRM}\)
6. \((15c^{8})^{-5}=(15)^{-5}.(c^{8})^{-5}=(\frac{1}{15})^{5}.(\frac{1}{c^{8}})^{5}=\text{ZRM}\left[=\frac{1}{759375} \frac{1}{c^{40}}\right]\)
7. \((\frac{8}{13})^{-1}.(\frac{14}{9})^{-1}=(\frac{8}{13}\frac{14}{9})^{-1}=(\frac{112}{117})^{-1}=(\frac{117}{112})^{1}=\left[\frac{117}{112}\right]\)
8. \((-\frac{6}{5})^{-4}=(-\frac{5}{6})^{4}=+\frac{5^{4}}{6^{4}}=\text{ZRM}= \left[=\frac{625}{1296}\right]\)
9. \((-3)^{-4}=(-\frac{1}{3})^{4}=+\frac{1^{4}}{3^{4}}=\text{ZRM}= \left[=\frac{1}{81}\right]\)
10. \((-4)^{-3}=(-\frac{1}{4})^{3}=-\frac{1^{3}}{4^{3}}=\text{ZRM}= \left[=-\frac{1}{64}\right]\)
11. \((-\frac{8}{5})^{-1}=(-\frac{5}{8})^{1}=-\frac{5^{1}}{8^{1}}= \left[=-\frac{5}{8}\right]\)
12. \((5c)^{6}.(5c)^{-9}=(5c)^{6+(-9)}=(5c)^{-3}=(\frac{1}{5}\frac{1}{c})^{3}\left[=\frac{1}{125} \frac{1}{c^{3}}\right]=\text{ZRM}\)