Rekenregels machten

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

1. \(-(-\frac{4}{3})^{-2}\)
2. \((\frac{19}{7}b)^{6}.(\frac{19}{7}b)^{-8}\)
3. \((2a)^{-7}.(2a)^{4}\)
4. \((\frac{16}{5}b)^{3}:(\frac{16}{5}b)^{2}\)
5. \((\frac{3}{2})^{10}.(\frac{3}{2})^{10}\)
6. \((9c)^{4}:(9c)^{9}\)
7. \((-\frac{19}{5})^{-2}\)
8. \((-\frac{10}{17})^{-6}\)
9. \(-(-\frac{5}{17})^{-6}\)
10. \((\frac{10}{19}c)^{5}:(\frac{10}{19}c)^{-9}\)
11. \((\frac{18}{17}a)^{-10}.(\frac{18}{17}a)^{10}\)
12. \((\frac{8}{5})^{-2}.(\frac{14}{9})^{-2}\)

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

Verbetersleutel

1. \(-(-\frac{4}{3})^{-2}=-(-\frac{3}{4})^{2}=-\frac{3^{2}}{4^{2}}\left[=-\frac{9}{16}\right]\)
2. \((\frac{19}{7}b)^{6}.(\frac{19}{7}b)^{-8}=(\frac{19}{7}b)^{6+(-8)}=(\frac{19}{7}b)^{-2}=(\frac{7}{19}\frac{1}{b})^{2}\left[=\frac{49}{361} \frac{1}{b^{2}}\right]\)
3. \((2a)^{-7}.(2a)^{4}=(2a)^{-7+4}=(2a)^{-3}=(\frac{1}{2}\frac{1}{a})^{3}\left[=\frac{1}{8} \frac{1}{a^{3}}\right]=\text{ZRM}\)
4. \((\frac{16}{5}b)^{3}:(\frac{16}{5}b)^{2}=(\frac{16}{5}b)^{3-2}=(\frac{16}{5}b)^{1}\left[ =\frac{16}{5}b^{1} \right]\)
5. \((\frac{3}{2})^{10}.(\frac{3}{2})^{10}=(\frac{3}{2}\frac{3}{2})^{10}=(\frac{9}{4})^{10}=\text{ZRM}=\left[\frac{3486784401}{1048576}\right]\)
6. \((9c)^{4}:(9c)^{9}=(9c)^{4-9}=(9c)^{-5}=(\frac{1}{9}\frac{1}{c})^{5}=\text{ZRM}\left[ =\frac{1}{59049} \frac{1}{c^{5}} \right]\)
7. \((-\frac{19}{5})^{-2}=(-\frac{5}{19})^{2}=+\frac{5^{2}}{19^{2}}= \left[=\frac{25}{361}\right]\)
8. \((-\frac{10}{17})^{-6}=(-\frac{17}{10})^{6}=+\frac{17^{6}}{10^{6}}=\text{ZRM}= \left[=\frac{24137569}{1000000}\right]\)
9. \(-(-\frac{5}{17})^{-6}=-(-\frac{17}{5})^{6}=-\frac{17^{6}}{5^{6}}=\text{ZRM}\left[=-\frac{24137569}{15625}\right]\)
10. \((\frac{10}{19}c)^{5}:(\frac{10}{19}c)^{-9}=(\frac{10}{19}c)^{5-(-9)}=(\frac{10}{19}c)^{14}=\text{ZRM}\left[ =\frac{100000000000000}{799006685782884121}c^{14} \right]\)
11. \((\frac{18}{17}a)^{-10}.(\frac{18}{17}a)^{10}=(\frac{18}{17}a)^{-10+10}=(\frac{18}{17}a)^{0}\left[=1a^{0}\right]\left[=1\right]\)
12. \((\frac{8}{5})^{-2}.(\frac{14}{9})^{-2}=(\frac{8}{5}\frac{14}{9})^{-2}=(\frac{112}{45})^{-2}=(\frac{45}{112})^{2}=\left[\frac{2025}{12544}\right]\)