Rekenregels machten

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

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

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

Verbetersleutel

1. \((-16y^{4})^{-5}=(-16)^{-5}.(y^{4})^{-5}=(\frac{1}{-16})^{5}.(\frac{1}{y^{4}})^{5}=\text{ZRM}\left[=(\frac{1}{-1048576}) \frac{1}{y^{20}}\right]\)
2. \((-\frac{7}{9})^{-4}=(-\frac{9}{7})^{4}=+\frac{9^{4}}{7^{4}}=\text{ZRM}= \left[=\frac{6561}{2401}\right]\)
3. \((\frac{11}{20})^{-9}.(\frac{19}{18})^{-9}=(\frac{11}{20}\frac{19}{18})^{-9}=(\frac{209}{360})^{-9}=(\frac{360}{209})^{9}=\text{ZRM}=\left[\frac{1.0155995666842E+23}{7.608807118921E+20}\right]\)
4. \((\frac{4}{7}c)^{-10}:(\frac{4}{7}c)^{-9}=(\frac{4}{7}c)^{-10-(-9)}=(\frac{4}{7}c)^{-1}=(\frac{7}{4}\frac{1}{c})^{1}\left[ =\frac{7}{4} \frac{1}{c^{1}} \right]\)
5. \(-(-2)^{-4}=-(-\frac{1}{2})^{4}=-\frac{1^{4}}{2^{4}}=\text{ZRM}\left[=-\frac{1}{16}\right]\)
6. \(-(-\frac{5}{14})^{-4}=-(-\frac{14}{5})^{4}=-\frac{14^{4}}{5^{4}}=\text{ZRM}\left[=-\frac{38416}{625}\right]\)
7. \((\frac{16}{19})^{2}.(\frac{2}{5})^{2}=(\frac{16}{19}\frac{2}{5})^{2}=(\frac{32}{95})^{2}=\left[\frac{1024}{9025}\right]\)
8. \((\frac{20}{11}b)^{-9}.(\frac{20}{11}b)^{2}=(\frac{20}{11}b)^{-9+2}=(\frac{20}{11}b)^{-7}=(\frac{11}{20}\frac{1}{b})^{7}\left[=\frac{19487171}{1280000000} \frac{1}{b^{7}}\right]=\text{ZRM}\)
9. \((-\frac{3}{10})^{-6}=(-\frac{10}{3})^{6}=+\frac{10^{6}}{3^{6}}=\text{ZRM}= \left[=\frac{1000000}{729}\right]\)
10. \(-(-\frac{2}{5})^{-1}=-(-\frac{5}{2})^{1}=+\frac{5^{1}}{2^{1}}\left[=\frac{5}{2}\right]\)
11. \(-(-\frac{10}{7})^{-6}=-(-\frac{7}{10})^{6}=-\frac{7^{6}}{10^{6}}=\text{ZRM}\left[=-\frac{117649}{1000000}\right]\)
12. \((\frac{19}{10}a)^{-7}.(\frac{19}{10}a)^{5}=(\frac{19}{10}a)^{-7+5}=(\frac{19}{10}a)^{-2}=(\frac{10}{19}\frac{1}{a})^{2}\left[=\frac{100}{361} \frac{1}{a^{2}}\right]\)