Rekenregels machten

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

1. \((8c)^{4}.(8c)^{-3}\)
2. \(-(-\frac{17}{6})^{-2}\)
3. \((\frac{4}{3}a)^{-2}.(\frac{4}{3}a)^{-3}\)
4. \((-10b^{5})^{5}\)
5. \((-\frac{19}{14})^{-1}\)
6. \((\frac{16}{3}a)^{-3}.(\frac{16}{3}a)^{-5}\)
7. \((-20c^{8})^{-10}\)
8. \((-10c^{5})^{6}\)
9. \((\frac{18}{19})^{7}.(\frac{18}{13})^{7}\)
10. \((\frac{7}{18})^{-7}.(\frac{8}{11})^{-7}\)
11. \((4)^{-1}.(\frac{4}{9})^{-1}\)
12. \((\frac{3}{2}b)^{-6}:(\frac{3}{2}b)^{4}\)

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

Verbetersleutel

1. \((8c)^{4}.(8c)^{-3}=(8c)^{4+(-3)}=(8c)^{1}\left[=8c^{1}\right]\)
2. \(-(-\frac{17}{6})^{-2}=-(-\frac{6}{17})^{2}=-\frac{6^{2}}{17^{2}}\left[=-\frac{36}{289}\right]\)
3. \((\frac{4}{3}a)^{-2}.(\frac{4}{3}a)^{-3}=(\frac{4}{3}a)^{-2+(-3)}=(\frac{4}{3}a)^{-5}=(\frac{3}{4}\frac{1}{a})^{5}\left[=\frac{243}{1024} \frac{1}{a^{5}}\right]=\text{ZRM}\)
4. \((-10b^{5})^{5}=(-10)^{5}.(b^{5})^{5}=\text{ZRM}\left[=(-100000)b^{25}\right]\)
5. \((-\frac{19}{14})^{-1}=(-\frac{14}{19})^{1}=-\frac{14^{1}}{19^{1}}= \left[=-\frac{14}{19}\right]\)
6. \((\frac{16}{3}a)^{-3}.(\frac{16}{3}a)^{-5}=(\frac{16}{3}a)^{-3+(-5)}=(\frac{16}{3}a)^{-8}=(\frac{3}{16}\frac{1}{a})^{8}\left[=\frac{6561}{4294967296} \frac{1}{a^{8}}\right]=\text{ZRM}\)
7. \((-20c^{8})^{-10}=(-20)^{-10}.(c^{8})^{-10}=(\frac{1}{-20})^{10}.(\frac{1}{c^{8}})^{10}=\text{ZRM}\left[=\frac{1}{10240000000000} \frac{1}{c^{80}}\right]\)
8. \((-10c^{5})^{6}=(-10)^{6}.(c^{5})^{6}=\text{ZRM}\left[=1000000c^{30}\right]\)
9. \((\frac{18}{19})^{7}.(\frac{18}{13})^{7}=(\frac{18}{19}\frac{18}{13})^{7}=(\frac{324}{247})^{7}=\text{ZRM}=\left[\frac{374813367582081024}{56089126010461063}\right]\)
10. \((\frac{7}{18})^{-7}.(\frac{8}{11})^{-7}=(\frac{7}{18}\frac{8}{11})^{-7}=(\frac{28}{99})^{-7}=(\frac{99}{28})^{7}=\text{ZRM}=\left[\frac{93206534790699}{13492928512}\right]\)
11. \((4)^{-1}.(\frac{4}{9})^{-1}=(4\frac{4}{9})^{-1}=(\frac{16}{9})^{-1}=(\frac{9}{16})^{1}=\left[\frac{9}{16}\right]\)
12. \((\frac{3}{2}b)^{-6}:(\frac{3}{2}b)^{4}=(\frac{3}{2}b)^{-6-4}=(\frac{3}{2}b)^{-10}=(\frac{2}{3}\frac{1}{b})^{10}=\text{ZRM}\left[ =\frac{1024}{59049} \frac{1}{b^{10}} \right]\)