Rekenregels machten

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

1. \((-\frac{17}{6})^{-5}\)
2. \((\frac{9}{2})^{-8}.(\frac{17}{6})^{-8}\)
3. \((17y^{8})^{-7}\)
4. \((\frac{19}{4})^{10}.(\frac{3}{4})^{10}\)
5. \((\frac{12}{17})^{5}.(\frac{3}{5})^{5}\)
6. \((-5)^{-5}\)
7. \((-10)^{-3}\)
8. \((-4)^{-2}\)
9. \((\frac{2}{3})^{-6}.(\frac{9}{10})^{-6}\)
10. \((\frac{6}{13}b)^{5}:(\frac{6}{13}b)^{-4}\)
11. \((\frac{6}{19})^{-7}.(\frac{10}{9})^{-7}\)
12. \((18y^{7})^{5}\)

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

Verbetersleutel

1. \((-\frac{17}{6})^{-5}=(-\frac{6}{17})^{5}=-\frac{6^{5}}{17^{5}}=\text{ZRM}= \left[=-\frac{7776}{1419857}\right]\)
2. \((\frac{9}{2})^{-8}.(\frac{17}{6})^{-8}=(\frac{9}{2}\frac{17}{6})^{-8}=(\frac{51}{4})^{-8}=(\frac{4}{51})^{8}=\text{ZRM}=\left[\frac{65536}{45767944570401}\right]\)
3. \((17y^{8})^{-7}=(17)^{-7}.(y^{8})^{-7}=(\frac{1}{17})^{7}.(\frac{1}{y^{8}})^{7}=\text{ZRM}\left[=\frac{1}{410338673} \frac{1}{y^{56}}\right]\)
4. \((\frac{19}{4})^{10}.(\frac{3}{4})^{10}=(\frac{19}{4}\frac{3}{4})^{10}=(\frac{57}{16})^{10}=\text{ZRM}=\left[\frac{362033331456891249}{1099511627776}\right]\)
5. \((\frac{12}{17})^{5}.(\frac{3}{5})^{5}=(\frac{12}{17}\frac{3}{5})^{5}=(\frac{36}{85})^{5}=\text{ZRM}=\left[\frac{60466176}{4437053125}\right]\)
6. \((-5)^{-5}=(-\frac{1}{5})^{5}=-\frac{1^{5}}{5^{5}}=\text{ZRM}= \left[=-\frac{1}{3125}\right]\)
7. \((-10)^{-3}=(-\frac{1}{10})^{3}=-\frac{1^{3}}{10^{3}}=\text{ZRM}= \left[=-\frac{1}{1000}\right]\)
8. \((-4)^{-2}=(-\frac{1}{4})^{2}=+\frac{1^{2}}{4^{2}}= \left[=\frac{1}{16}\right]\)
9. \((\frac{2}{3})^{-6}.(\frac{9}{10})^{-6}=(\frac{2}{3}\frac{9}{10})^{-6}=(\frac{3}{5})^{-6}=(\frac{5}{3})^{6}=\text{ZRM}=\left[\frac{15625}{729}\right]\)
10. \((\frac{6}{13}b)^{5}:(\frac{6}{13}b)^{-4}=(\frac{6}{13}b)^{5-(-4)}=(\frac{6}{13}b)^{9}=\text{ZRM}\left[ =\frac{10077696}{10604499373}b^{9} \right]\)
11. \((\frac{6}{19})^{-7}.(\frac{10}{9})^{-7}=(\frac{6}{19}\frac{10}{9})^{-7}=(\frac{20}{57})^{-7}=(\frac{57}{20})^{7}=\text{ZRM}=\left[\frac{1954897493193}{1280000000}\right]\)
12. \((18y^{7})^{5}=(18)^{5}.(y^{7})^{5}=\text{ZRM}\left[=1889568y^{35}\right]\)