Rekenregels machten

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

1. \((\frac{17}{20})^{6}.(\frac{9}{4})^{6}\)
2. \((\frac{16}{17}a)^{6}:(\frac{16}{17}a)^{-9}\)
3. \((\frac{13}{3})^{-3}.(\frac{13}{10})^{-3}\)
4. \((-\frac{2}{9})^{-5}\)
5. \((-16c^{6})^{2}\)
6. \((-\frac{9}{16})^{-5}\)
7. \((-\frac{5}{6})^{-3}\)
8. \((\frac{16}{5}a)^{4}.(\frac{16}{5}a)^{8}\)
9. \((\frac{8}{9}y)^{-4}:(\frac{8}{9}y)^{7}\)
10. \((\frac{19}{12})^{10}.(\frac{13}{16})^{10}\)
11. \((-\frac{13}{7})^{-5}\)
12. \((\frac{4}{7}c)^{3}.(\frac{4}{7}c)^{-5}\)

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

Verbetersleutel

1. \((\frac{17}{20})^{6}.(\frac{9}{4})^{6}=(\frac{17}{20}\frac{9}{4})^{6}=(\frac{153}{80})^{6}=\text{ZRM}=\left[\frac{12827693806929}{262144000000}\right]\)
2. \((\frac{16}{17}a)^{6}:(\frac{16}{17}a)^{-9}=(\frac{16}{17}a)^{6-(-9)}=(\frac{16}{17}a)^{15}=\text{ZRM}\left[ =\frac{1152921504606846976}{2862423051509815793}a^{15} \right]\)
3. \((\frac{13}{3})^{-3}.(\frac{13}{10})^{-3}=(\frac{13}{3}\frac{13}{10})^{-3}=(\frac{169}{30})^{-3}=(\frac{30}{169})^{3}=\text{ZRM}=\left[\frac{27000}{4826809}\right]\)
4. \((-\frac{2}{9})^{-5}=(-\frac{9}{2})^{5}=-\frac{9^{5}}{2^{5}}=\text{ZRM}= \left[=-\frac{59049}{32}\right]\)
5. \((-16c^{6})^{2}=(-16)^{2}.(c^{6})^{2}=\text{ZRM}\left[=256c^{12}\right]\)
6. \((-\frac{9}{16})^{-5}=(-\frac{16}{9})^{5}=-\frac{16^{5}}{9^{5}}=\text{ZRM}= \left[=-\frac{1048576}{59049}\right]\)
7. \((-\frac{5}{6})^{-3}=(-\frac{6}{5})^{3}=-\frac{6^{3}}{5^{3}}=\text{ZRM}= \left[=-\frac{216}{125}\right]\)
8. \((\frac{16}{5}a)^{4}.(\frac{16}{5}a)^{8}=(\frac{16}{5}a)^{4+8}=(\frac{16}{5}a)^{12}\left[=\frac{281474976710656}{244140625}a^{12}\right]=\text{ZRM}\)
9. \((\frac{8}{9}y)^{-4}:(\frac{8}{9}y)^{7}=(\frac{8}{9}y)^{-4-7}=(\frac{8}{9}y)^{-11}=(\frac{9}{8}\frac{1}{y})^{11}=\text{ZRM}\left[ =\frac{31381059609}{8589934592} \frac{1}{y^{11}} \right]\)
10. \((\frac{19}{12})^{10}.(\frac{13}{16})^{10}=(\frac{19}{12}\frac{13}{16})^{10}=(\frac{247}{192})^{10}=\text{ZRM}=\left[\frac{8.4521954772674E+23}{6.807886192553E+22}\right]\)
11. \((-\frac{13}{7})^{-5}=(-\frac{7}{13})^{5}=-\frac{7^{5}}{13^{5}}=\text{ZRM}= \left[=-\frac{16807}{371293}\right]\)
12. \((\frac{4}{7}c)^{3}.(\frac{4}{7}c)^{-5}=(\frac{4}{7}c)^{3+(-5)}=(\frac{4}{7}c)^{-2}=(\frac{7}{4}\frac{1}{c})^{2}\left[=\frac{49}{16} \frac{1}{c^{2}}\right]\)