Rekenregels machten

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

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

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

Verbetersleutel

1. \((12a^{2})^{-3}=(12)^{-3}.(a^{2})^{-3}=(\frac{1}{12})^{3}.(\frac{1}{a^{2}})^{3}=\text{ZRM}\left[=\frac{1}{1728} \frac{1}{a^{6}}\right]\)
2. \((\frac{11}{18}a)^{-1}.(\frac{11}{18}a)^{3}=(\frac{11}{18}a)^{-1+3}=(\frac{11}{18}a)^{2}\left[=\frac{121}{324}a^{2}\right]\)
3. \((6)^{-7}.(12)^{-7}=(612)^{-7}=(72)^{-7}=(\frac{1}{72})^{7}=\text{ZRM}=\left[\frac{1}{10030613004288}\right]\)
4. \((-6c^{9})^{-5}=(-6)^{-5}.(c^{9})^{-5}=(\frac{1}{-6})^{5}.(\frac{1}{c^{9}})^{5}=\text{ZRM}\left[=(\frac{1}{-7776}) \frac{1}{c^{45}}\right]\)
5. \((9y^{6})^{6}=(9)^{6}.(y^{6})^{6}=\text{ZRM}\left[=531441y^{36}\right]\)
6. \((-\frac{10}{13})^{-2}=(-\frac{13}{10})^{2}=+\frac{13^{2}}{10^{2}}= \left[=\frac{169}{100}\right]\)
7. \(-(-\frac{7}{3})^{-6}=-(-\frac{3}{7})^{6}=-\frac{3^{6}}{7^{6}}=\text{ZRM}\left[=-\frac{729}{117649}\right]\)
8. \(-(-\frac{8}{11})^{-1}=-(-\frac{11}{8})^{1}=+\frac{11^{1}}{8^{1}}\left[=\frac{11}{8}\right]\)
9. \((-13b^{3})^{8}=(-13)^{8}.(b^{3})^{8}=\text{ZRM}\left[=815730721b^{24}\right]\)
10. \((\frac{4}{9}b)^{-5}:(\frac{4}{9}b)^{5}=(\frac{4}{9}b)^{-5-5}=(\frac{4}{9}b)^{-10}=(\frac{9}{4}\frac{1}{b})^{10}=\text{ZRM}\left[ =\frac{3486784401}{1048576} \frac{1}{b^{10}} \right]\)
11. \((\frac{19}{8}a)^{-6}.(\frac{19}{8}a)^{-7}=(\frac{19}{8}a)^{-6+(-7)}=(\frac{19}{8}a)^{-13}=(\frac{8}{19}\frac{1}{a})^{13}\left[=\frac{549755813888}{42052983462257059} \frac{1}{a^{13}}\right]=\text{ZRM}\)
12. \((\frac{3}{4}a)^{9}:(\frac{3}{4}a)^{6}=(\frac{3}{4}a)^{9-6}=(\frac{3}{4}a)^{3}=\text{ZRM}\left[ =\frac{27}{64}a^{3} \right]\)