Rekenregels machten

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

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

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

Verbetersleutel

1. \((-7b^{2})^{7}=(-7)^{7}.(b^{2})^{7}=\text{ZRM}\left[=(-823543)b^{14}\right]\)
2. \((20a^{5})^{2}=(20)^{2}.(a^{5})^{2}=\text{ZRM}\left[=400a^{10}\right]\)
3. \((\frac{9}{10}c)^{2}.(\frac{9}{10}c)^{-4}=(\frac{9}{10}c)^{2+(-4)}=(\frac{9}{10}c)^{-2}=(\frac{10}{9}\frac{1}{c})^{2}\left[=\frac{100}{81} \frac{1}{c^{2}}\right]\)
4. \((-10)^{-5}=(-\frac{1}{10})^{5}=-\frac{1^{5}}{10^{5}}=\text{ZRM}= \left[=-\frac{1}{100000}\right]\)
5. \((\frac{8}{13}c)^{-9}.(\frac{8}{13}c)^{1}=(\frac{8}{13}c)^{-9+1}=(\frac{8}{13}c)^{-8}=(\frac{13}{8}\frac{1}{c})^{8}\left[=\frac{815730721}{16777216} \frac{1}{c^{8}}\right]=\text{ZRM}\)
6. \((\frac{11}{2}b)^{-8}:(\frac{11}{2}b)^{-10}=(\frac{11}{2}b)^{-8-(-10)}=(\frac{11}{2}b)^{2}\left[ =\frac{121}{4}b^{2} \right]\)
7. \((-18a^{7})^{-9}=(-18)^{-9}.(a^{7})^{-9}=(\frac{1}{-18})^{9}.(\frac{1}{a^{7}})^{9}=\text{ZRM}\left[=(\frac{1}{-198359290368}) \frac{1}{a^{63}}\right]\)
8. \((\frac{19}{2})^{4}.(2)^{4}=(\frac{19}{2}2)^{4}=(19)^{4}=\text{ZRM}=\left[130321\right]\)
9. \((-\frac{4}{19})^{-3}=(-\frac{19}{4})^{3}=-\frac{19^{3}}{4^{3}}=\text{ZRM}= \left[=-\frac{6859}{64}\right]\)
10. \((\frac{13}{12})^{-4}.(\frac{6}{13})^{-4}=(\frac{13}{12}\frac{6}{13})^{-4}=(\frac{1}{2})^{-4}=(2)^{4}=\text{ZRM}=\left[16\right]\)
11. \(-(-5)^{-6}=-(-\frac{1}{5})^{6}=-\frac{1^{6}}{5^{6}}=\text{ZRM}\left[=-\frac{1}{15625}\right]\)
12. \((-10x^{9})^{-7}=(-10)^{-7}.(x^{9})^{-7}=(\frac{1}{-10})^{7}.(\frac{1}{x^{9}})^{7}=\text{ZRM}\left[=(\frac{1}{-10000000}) \frac{1}{x^{63}}\right]\)