Rekenregels machten

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

1. \((\frac{19}{12})^{7}.(\frac{2}{7})^{7}\)
2. \((\frac{4}{7}a)^{10}.(\frac{4}{7}a)^{7}\)
3. \((-\frac{5}{8})^{-2}\)
4. \((\frac{5}{19})^{-9}.(\frac{4}{13})^{-9}\)
5. \((-6)^{-3}\)
6. \((-\frac{4}{3})^{-5}\)
7. \((\frac{2}{7})^{-1}.(\frac{16}{19})^{-1}\)
8. \((\frac{10}{9})^{4}.(3)^{4}\)
9. \((\frac{8}{7}a)^{-4}.(\frac{8}{7}a)^{7}\)
10. \((\frac{15}{13}c)^{-1}:(\frac{15}{13}c)^{-8}\)
11. \((\frac{19}{12}y)^{-2}.(\frac{19}{12}y)^{-8}\)
12. \((\frac{12}{5})^{-5}.(\frac{20}{9})^{-5}\)

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

Verbetersleutel

1. \((\frac{19}{12})^{7}.(\frac{2}{7})^{7}=(\frac{19}{12}\frac{2}{7})^{7}=(\frac{19}{42})^{7}=\text{ZRM}=\left[\frac{893871739}{230539333248}\right]\)
2. \((\frac{4}{7}a)^{10}.(\frac{4}{7}a)^{7}=(\frac{4}{7}a)^{10+7}=(\frac{4}{7}a)^{17}\left[=\frac{17179869184}{232630513987207}a^{17}\right]=\text{ZRM}\)
3. \((-\frac{5}{8})^{-2}=(-\frac{8}{5})^{2}=+\frac{8^{2}}{5^{2}}= \left[=\frac{64}{25}\right]\)
4. \((\frac{5}{19})^{-9}.(\frac{4}{13})^{-9}=(\frac{5}{19}\frac{4}{13})^{-9}=(\frac{20}{247})^{-9}=(\frac{247}{20})^{9}=\text{ZRM}=\left[\frac{3.4219414887722E+21}{512000000000}\right]\)
5. \((-6)^{-3}=(-\frac{1}{6})^{3}=-\frac{1^{3}}{6^{3}}=\text{ZRM}= \left[=-\frac{1}{216}\right]\)
6. \((-\frac{4}{3})^{-5}=(-\frac{3}{4})^{5}=-\frac{3^{5}}{4^{5}}=\text{ZRM}= \left[=-\frac{243}{1024}\right]\)
7. \((\frac{2}{7})^{-1}.(\frac{16}{19})^{-1}=(\frac{2}{7}\frac{16}{19})^{-1}=(\frac{32}{133})^{-1}=(\frac{133}{32})^{1}=\left[\frac{133}{32}\right]\)
8. \((\frac{10}{9})^{4}.(3)^{4}=(\frac{10}{9}3)^{4}=(\frac{10}{3})^{4}=\text{ZRM}=\left[\frac{10000}{81}\right]\)
9. \((\frac{8}{7}a)^{-4}.(\frac{8}{7}a)^{7}=(\frac{8}{7}a)^{-4+7}=(\frac{8}{7}a)^{3}\left[=\frac{512}{343}a^{3}\right]=\text{ZRM}\)
10. \((\frac{15}{13}c)^{-1}:(\frac{15}{13}c)^{-8}=(\frac{15}{13}c)^{-1-(-8)}=(\frac{15}{13}c)^{7}=\text{ZRM}\left[ =\frac{170859375}{62748517}c^{7} \right]\)
11. \((\frac{19}{12}y)^{-2}.(\frac{19}{12}y)^{-8}=(\frac{19}{12}y)^{-2+(-8)}=(\frac{19}{12}y)^{-10}=(\frac{12}{19}\frac{1}{y})^{10}\left[=\frac{61917364224}{6131066257801} \frac{1}{y^{10}}\right]=\text{ZRM}\)
12. \((\frac{12}{5})^{-5}.(\frac{20}{9})^{-5}=(\frac{12}{5}\frac{20}{9})^{-5}=(\frac{16}{3})^{-5}=(\frac{3}{16})^{5}=\text{ZRM}=\left[\frac{243}{1048576}\right]\)