Rekenregels machten

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

1. \(-(-\frac{20}{17})^{-6}\)
2. \((\frac{12}{19}b)^{9}.(\frac{12}{19}b)^{1}\)
3. \((-10)^{-6}\)
4. \((\frac{12}{7}y)^{5}.(\frac{12}{7}y)^{-5}\)
5. \((-\frac{3}{11})^{-2}\)
6. \((10a^{3})^{10}\)
7. \((\frac{5}{17}y)^{9}.(\frac{5}{17}y)^{4}\)
8. \((\frac{17}{7})^{5}.(\frac{9}{8})^{5}\)
9. \(-(-\frac{11}{6})^{-6}\)
10. \((\frac{5}{3}x)^{6}.(\frac{5}{3}x)^{-1}\)
11. \((-17y^{6})^{-7}\)
12. \((-17b^{4})^{5}\)

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

Verbetersleutel

1. \(-(-\frac{20}{17})^{-6}=-(-\frac{17}{20})^{6}=-\frac{17^{6}}{20^{6}}=\text{ZRM}\left[=-\frac{24137569}{64000000}\right]\)
2. \((\frac{12}{19}b)^{9}.(\frac{12}{19}b)^{1}=(\frac{12}{19}b)^{9+1}=(\frac{12}{19}b)^{10}\left[=\frac{61917364224}{6131066257801}b^{10}\right]=\text{ZRM}\)
3. \((-10)^{-6}=(-\frac{1}{10})^{6}=+\frac{1^{6}}{10^{6}}=\text{ZRM}= \left[=\frac{1}{1000000}\right]\)
4. \((\frac{12}{7}y)^{5}.(\frac{12}{7}y)^{-5}=(\frac{12}{7}y)^{5+(-5)}=(\frac{12}{7}y)^{0}\left[=1y^{0}\right]\left[=1\right]\)
5. \((-\frac{3}{11})^{-2}=(-\frac{11}{3})^{2}=+\frac{11^{2}}{3^{2}}= \left[=\frac{121}{9}\right]\)
6. \((10a^{3})^{10}=(10)^{10}.(a^{3})^{10}=\text{ZRM}\left[=10000000000a^{30}\right]\)
7. \((\frac{5}{17}y)^{9}.(\frac{5}{17}y)^{4}=(\frac{5}{17}y)^{9+4}=(\frac{5}{17}y)^{13}\left[=\frac{1220703125}{9904578032905937}y^{13}\right]=\text{ZRM}\)
8. \((\frac{17}{7})^{5}.(\frac{9}{8})^{5}=(\frac{17}{7}\frac{9}{8})^{5}=(\frac{153}{56})^{5}=\text{ZRM}=\left[\frac{83841135993}{550731776}\right]\)
9. \(-(-\frac{11}{6})^{-6}=-(-\frac{6}{11})^{6}=-\frac{6^{6}}{11^{6}}=\text{ZRM}\left[=-\frac{46656}{1771561}\right]\)
10. \((\frac{5}{3}x)^{6}.(\frac{5}{3}x)^{-1}=(\frac{5}{3}x)^{6+(-1)}=(\frac{5}{3}x)^{5}\left[=\frac{3125}{243}x^{5}\right]=\text{ZRM}\)
11. \((-17y^{6})^{-7}=(-17)^{-7}.(y^{6})^{-7}=(\frac{1}{-17})^{7}.(\frac{1}{y^{6}})^{7}=\text{ZRM}\left[=(\frac{1}{-410338673}) \frac{1}{y^{42}}\right]\)
12. \((-17b^{4})^{5}=(-17)^{5}.(b^{4})^{5}=\text{ZRM}\left[=(-1419857)b^{20}\right]\)