Rekenregels machten

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

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

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

Verbetersleutel

1. \(-(-\frac{8}{19})^{-5}=-(-\frac{19}{8})^{5}=+\frac{19^{5}}{8^{5}}=\text{ZRM}\left[=\frac{2476099}{32768}\right]\)
2. \(-(-\frac{4}{7})^{-3}=-(-\frac{7}{4})^{3}=+\frac{7^{3}}{4^{3}}=\text{ZRM}\left[=\frac{343}{64}\right]\)
3. \((-\frac{3}{5})^{-3}=(-\frac{5}{3})^{3}=-\frac{5^{3}}{3^{3}}=\text{ZRM}= \left[=-\frac{125}{27}\right]\)
4. \((-\frac{4}{5})^{-2}=(-\frac{5}{4})^{2}=+\frac{5^{2}}{4^{2}}= \left[=\frac{25}{16}\right]\)
5. \((\frac{7}{2}c)^{-1}:(\frac{7}{2}c)^{-3}=(\frac{7}{2}c)^{-1-(-3)}=(\frac{7}{2}c)^{2}\left[ =\frac{49}{4}c^{2} \right]\)
6. \((2)^{-10}.(\frac{3}{4})^{-10}=(2\frac{3}{4})^{-10}=(\frac{3}{2})^{-10}=(\frac{2}{3})^{10}=\text{ZRM}=\left[\frac{1024}{59049}\right]\)
7. \((\frac{7}{8}x)^{-8}:(\frac{7}{8}x)^{-6}=(\frac{7}{8}x)^{-8-(-6)}=(\frac{7}{8}x)^{-2}=(\frac{8}{7}\frac{1}{x})^{2}\left[ =\frac{64}{49} \frac{1}{x^{2}} \right]\)
8. \((-\frac{9}{19})^{-1}=(-\frac{19}{9})^{1}=-\frac{19^{1}}{9^{1}}= \left[=-\frac{19}{9}\right]\)
9. \((7c^{10})^{9}=(7)^{9}.(c^{10})^{9}=\text{ZRM}\left[=40353607c^{90}\right]\)
10. \(-(-\frac{13}{8})^{-1}=-(-\frac{8}{13})^{1}=+\frac{8^{1}}{13^{1}}\left[=\frac{8}{13}\right]\)
11. \((\frac{17}{10})^{7}.(\frac{11}{7})^{7}=(\frac{17}{10}\frac{11}{7})^{7}=(\frac{187}{70})^{7}=\text{ZRM}=\left[\frac{7996339888664083}{8235430000000}\right]\)
12. \((\frac{6}{7})^{-2}.(\frac{7}{11})^{-2}=(\frac{6}{7}\frac{7}{11})^{-2}=(\frac{6}{11})^{-2}=(\frac{11}{6})^{2}=\left[\frac{121}{36}\right]\)