Rekenregels machten

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

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

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

Verbetersleutel

1. \(-(-\frac{19}{2})^{-2}=-(-\frac{2}{19})^{2}=-\frac{2^{2}}{19^{2}}\left[=-\frac{4}{361}\right]\)
2. \(-(-\frac{17}{19})^{-5}=-(-\frac{19}{17})^{5}=+\frac{19^{5}}{17^{5}}=\text{ZRM}\left[=\frac{2476099}{1419857}\right]\)
3. \(-(-\frac{12}{19})^{-3}=-(-\frac{19}{12})^{3}=+\frac{19^{3}}{12^{3}}=\text{ZRM}\left[=\frac{6859}{1728}\right]\)
4. \((-\frac{9}{19})^{-5}=(-\frac{19}{9})^{5}=-\frac{19^{5}}{9^{5}}=\text{ZRM}= \left[=-\frac{2476099}{59049}\right]\)
5. \((\frac{11}{16}x)^{-6}.(\frac{11}{16}x)^{-1}=(\frac{11}{16}x)^{-6+(-1)}=(\frac{11}{16}x)^{-7}=(\frac{16}{11}\frac{1}{x})^{7}\left[=\frac{268435456}{19487171} \frac{1}{x^{7}}\right]=\text{ZRM}\)
6. \((-12x^{5})^{-8}=(-12)^{-8}.(x^{5})^{-8}=(\frac{1}{-12})^{8}.(\frac{1}{x^{5}})^{8}=\text{ZRM}\left[=\frac{1}{429981696} \frac{1}{x^{40}}\right]\)
7. \((2c)^{-6}:(2c)^{4}=(2c)^{-6-4}=(2c)^{-10}=(\frac{1}{2}\frac{1}{c})^{10}=\text{ZRM}\left[ =\frac{1}{1024} \frac{1}{c^{10}} \right]\)
8. \((\frac{16}{19}a)^{-6}.(\frac{16}{19}a)^{4}=(\frac{16}{19}a)^{-6+4}=(\frac{16}{19}a)^{-2}=(\frac{19}{16}\frac{1}{a})^{2}\left[=\frac{361}{256} \frac{1}{a^{2}}\right]\)
9. \((-\frac{11}{14})^{-4}=(-\frac{14}{11})^{4}=+\frac{14^{4}}{11^{4}}=\text{ZRM}= \left[=\frac{38416}{14641}\right]\)
10. \((4x)^{6}.(4x)^{7}=(4x)^{6+7}=(4x)^{13}\left[=67108864x^{13}\right]=\text{ZRM}\)
11. \((\frac{9}{20})^{-3}.(\frac{12}{17})^{-3}=(\frac{9}{20}\frac{12}{17})^{-3}=(\frac{27}{85})^{-3}=(\frac{85}{27})^{3}=\text{ZRM}=\left[\frac{614125}{19683}\right]\)
12. \(-(-\frac{5}{9})^{-6}=-(-\frac{9}{5})^{6}=-\frac{9^{6}}{5^{6}}=\text{ZRM}\left[=-\frac{531441}{15625}\right]\)