Rekenregels machten

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

1. \(-(-5)^{-3}\)
2. \(-(-\frac{5}{3})^{-3}\)
3. \((\frac{17}{6}b)^{4}:(\frac{17}{6}b)^{-5}\)
4. \(-(-\frac{19}{8})^{-5}\)
5. \((-\frac{3}{2})^{-6}\)
6. \((5y^{5})^{-8}\)
7. \((\frac{15}{11}x)^{5}.(\frac{15}{11}x)^{-2}\)
8. \((3b^{7})^{-7}\)
9. \((-\frac{6}{7})^{-4}\)
10. \((\frac{14}{11}x)^{10}.(\frac{14}{11}x)^{-7}\)
11. \((-3)^{-5}\)
12. \((-1x^{4})^{-4}\)

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

Verbetersleutel

1. \(-(-5)^{-3}=-(-\frac{1}{5})^{3}=+\frac{1^{3}}{5^{3}}=\text{ZRM}\left[=\frac{1}{125}\right]\)
2. \(-(-\frac{5}{3})^{-3}=-(-\frac{3}{5})^{3}=+\frac{3^{3}}{5^{3}}=\text{ZRM}\left[=\frac{27}{125}\right]\)
3. \((\frac{17}{6}b)^{4}:(\frac{17}{6}b)^{-5}=(\frac{17}{6}b)^{4-(-5)}=(\frac{17}{6}b)^{9}=\text{ZRM}\left[ =\frac{118587876497}{10077696}b^{9} \right]\)
4. \(-(-\frac{19}{8})^{-5}=-(-\frac{8}{19})^{5}=+\frac{8^{5}}{19^{5}}=\text{ZRM}\left[=\frac{32768}{2476099}\right]\)
5. \((-\frac{3}{2})^{-6}=(-\frac{2}{3})^{6}=+\frac{2^{6}}{3^{6}}=\text{ZRM}= \left[=\frac{64}{729}\right]\)
6. \((5y^{5})^{-8}=(5)^{-8}.(y^{5})^{-8}=(\frac{1}{5})^{8}.(\frac{1}{y^{5}})^{8}=\text{ZRM}\left[=\frac{1}{390625} \frac{1}{y^{40}}\right]\)
7. \((\frac{15}{11}x)^{5}.(\frac{15}{11}x)^{-2}=(\frac{15}{11}x)^{5+(-2)}=(\frac{15}{11}x)^{3}\left[=\frac{3375}{1331}x^{3}\right]=\text{ZRM}\)
8. \((3b^{7})^{-7}=(3)^{-7}.(b^{7})^{-7}=(\frac{1}{3})^{7}.(\frac{1}{b^{7}})^{7}=\text{ZRM}\left[=\frac{1}{2187} \frac{1}{b^{49}}\right]\)
9. \((-\frac{6}{7})^{-4}=(-\frac{7}{6})^{4}=+\frac{7^{4}}{6^{4}}=\text{ZRM}= \left[=\frac{2401}{1296}\right]\)
10. \((\frac{14}{11}x)^{10}.(\frac{14}{11}x)^{-7}=(\frac{14}{11}x)^{10+(-7)}=(\frac{14}{11}x)^{3}\left[=\frac{2744}{1331}x^{3}\right]=\text{ZRM}\)
11. \((-3)^{-5}=(-\frac{1}{3})^{5}=-\frac{1^{5}}{3^{5}}=\text{ZRM}= \left[=-\frac{1}{243}\right]\)
12. \((-1x^{4})^{-4}=(-1)^{-4}.(x^{4})^{-4}=(\frac{1}{-1})^{4}.(\frac{1}{x^{4}})^{4}=\text{ZRM}\left[=1 \frac{1}{x^{16}}\right]\)