Rekenregels machten

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

1. \(-(-\frac{4}{7})^{-6}\)
2. \((-\frac{6}{7})^{-3}\)
3. \((\frac{13}{11}b)^{-10}:(\frac{13}{11}b)^{-4}\)
4. \((\frac{9}{7}x)^{-5}.(\frac{9}{7}x)^{10}\)
5. \((\frac{5}{17}y)^{-5}:(\frac{5}{17}y)^{8}\)
6. \((-\frac{9}{16})^{-5}\)
7. \((\frac{8}{5}b)^{7}:(\frac{8}{5}b)^{-9}\)
8. \((\frac{17}{2})^{-3}.(4)^{-3}\)
9. \(-(-\frac{8}{3})^{-1}\)
10. \((\frac{4}{3}x)^{-9}:(\frac{4}{3}x)^{10}\)
11. \(-(-\frac{19}{9})^{-1}\)
12. \((2)^{1}.(7)^{1}\)

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

Verbetersleutel

1. \(-(-\frac{4}{7})^{-6}=-(-\frac{7}{4})^{6}=-\frac{7^{6}}{4^{6}}=\text{ZRM}\left[=-\frac{117649}{4096}\right]\)
2. \((-\frac{6}{7})^{-3}=(-\frac{7}{6})^{3}=-\frac{7^{3}}{6^{3}}=\text{ZRM}= \left[=-\frac{343}{216}\right]\)
3. \((\frac{13}{11}b)^{-10}:(\frac{13}{11}b)^{-4}=(\frac{13}{11}b)^{-10-(-4)}=(\frac{13}{11}b)^{-6}=(\frac{11}{13}\frac{1}{b})^{6}=\text{ZRM}\left[ =\frac{1771561}{4826809} \frac{1}{b^{6}} \right]\)
4. \((\frac{9}{7}x)^{-5}.(\frac{9}{7}x)^{10}=(\frac{9}{7}x)^{-5+10}=(\frac{9}{7}x)^{5}\left[=\frac{59049}{16807}x^{5}\right]=\text{ZRM}\)
5. \((\frac{5}{17}y)^{-5}:(\frac{5}{17}y)^{8}=(\frac{5}{17}y)^{-5-8}=(\frac{5}{17}y)^{-13}=(\frac{17}{5}\frac{1}{y})^{13}=\text{ZRM}\left[ =\frac{9904578032905937}{1220703125} \frac{1}{y^{13}} \right]\)
6. \((-\frac{9}{16})^{-5}=(-\frac{16}{9})^{5}=-\frac{16^{5}}{9^{5}}=\text{ZRM}= \left[=-\frac{1048576}{59049}\right]\)
7. \((\frac{8}{5}b)^{7}:(\frac{8}{5}b)^{-9}=(\frac{8}{5}b)^{7-(-9)}=(\frac{8}{5}b)^{16}=\text{ZRM}\left[ =\frac{281474976710656}{152587890625}b^{16} \right]\)
8. \((\frac{17}{2})^{-3}.(4)^{-3}=(\frac{17}{2}4)^{-3}=(34)^{-3}=(\frac{1}{34})^{3}=\text{ZRM}=\left[\frac{1}{39304}\right]\)
9. \(-(-\frac{8}{3})^{-1}=-(-\frac{3}{8})^{1}=+\frac{3^{1}}{8^{1}}\left[=\frac{3}{8}\right]\)
10. \((\frac{4}{3}x)^{-9}:(\frac{4}{3}x)^{10}=(\frac{4}{3}x)^{-9-10}=(\frac{4}{3}x)^{-19}=(\frac{3}{4}\frac{1}{x})^{19}=\text{ZRM}\left[ =\frac{1162261467}{274877906944} \frac{1}{x^{19}} \right]\)
11. \(-(-\frac{19}{9})^{-1}=-(-\frac{9}{19})^{1}=+\frac{9^{1}}{19^{1}}\left[=\frac{9}{19}\right]\)
12. \((2)^{1}.(7)^{1}=(27)^{1}=(14)^{1}=\left[14\right]\)