Rekenregels machten

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

1. \((\frac{17}{2})^{-9}.(\frac{12}{17})^{-9}\)
2. \((\frac{2}{7})^{3}.(\frac{11}{12})^{3}\)
3. \((\frac{13}{8})^{6}.(\frac{19}{6})^{6}\)
4. \(-(-\frac{10}{7})^{-2}\)
5. \((-8y^{2})^{-7}\)
6. \((\frac{10}{7})^{-1}.(2)^{-1}\)
7. \((-\frac{7}{15})^{-1}\)
8. \(-(-\frac{4}{9})^{-4}\)
9. \(-(-\frac{13}{2})^{-1}\)
10. \((-\frac{4}{3})^{-2}\)
11. \((5c)^{-2}.(5c)^{-6}\)
12. \((10x^{5})^{-10}\)

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

Verbetersleutel

1. \((\frac{17}{2})^{-9}.(\frac{12}{17})^{-9}=(\frac{17}{2}\frac{12}{17})^{-9}=(6)^{-9}=(\frac{1}{6})^{9}=\text{ZRM}=\left[\frac{1}{10077696}\right]\)
2. \((\frac{2}{7})^{3}.(\frac{11}{12})^{3}=(\frac{2}{7}\frac{11}{12})^{3}=(\frac{11}{42})^{3}=\text{ZRM}=\left[\frac{1331}{74088}\right]\)
3. \((\frac{13}{8})^{6}.(\frac{19}{6})^{6}=(\frac{13}{8}\frac{19}{6})^{6}=(\frac{247}{48})^{6}=\text{ZRM}=\left[\frac{227081481823729}{12230590464}\right]\)
4. \(-(-\frac{10}{7})^{-2}=-(-\frac{7}{10})^{2}=-\frac{7^{2}}{10^{2}}\left[=-\frac{49}{100}\right]\)
5. \((-8y^{2})^{-7}=(-8)^{-7}.(y^{2})^{-7}=(\frac{1}{-8})^{7}.(\frac{1}{y^{2}})^{7}=\text{ZRM}\left[=(\frac{1}{-2097152}) \frac{1}{y^{14}}\right]\)
6. \((\frac{10}{7})^{-1}.(2)^{-1}=(\frac{10}{7}2)^{-1}=(\frac{20}{7})^{-1}=(\frac{7}{20})^{1}=\left[\frac{7}{20}\right]\)
7. \((-\frac{7}{15})^{-1}=(-\frac{15}{7})^{1}=-\frac{15^{1}}{7^{1}}= \left[=-\frac{15}{7}\right]\)
8. \(-(-\frac{4}{9})^{-4}=-(-\frac{9}{4})^{4}=-\frac{9^{4}}{4^{4}}=\text{ZRM}\left[=-\frac{6561}{256}\right]\)
9. \(-(-\frac{13}{2})^{-1}=-(-\frac{2}{13})^{1}=+\frac{2^{1}}{13^{1}}\left[=\frac{2}{13}\right]\)
10. \((-\frac{4}{3})^{-2}=(-\frac{3}{4})^{2}=+\frac{3^{2}}{4^{2}}= \left[=\frac{9}{16}\right]\)
11. \((5c)^{-2}.(5c)^{-6}=(5c)^{-2+(-6)}=(5c)^{-8}=(\frac{1}{5}\frac{1}{c})^{8}\left[=\frac{1}{390625} \frac{1}{c^{8}}\right]=\text{ZRM}\)
12. \((10x^{5})^{-10}=(10)^{-10}.(x^{5})^{-10}=(\frac{1}{10})^{10}.(\frac{1}{x^{5}})^{10}=\text{ZRM}\left[=\frac{1}{10000000000} \frac{1}{x^{50}}\right]\)