Rekenregels machten

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

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

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

Verbetersleutel

1. \((-3a^{3})^{10}=(-3)^{10}.(a^{3})^{10}=\text{ZRM}\left[=59049a^{30}\right]\)
2. \((-\frac{4}{3})^{-4}=(-\frac{3}{4})^{4}=+\frac{3^{4}}{4^{4}}=\text{ZRM}= \left[=\frac{81}{256}\right]\)
3. \((\frac{5}{4}y)^{5}.(\frac{5}{4}y)^{7}=(\frac{5}{4}y)^{5+7}=(\frac{5}{4}y)^{12}\left[=\frac{244140625}{16777216}y^{12}\right]=\text{ZRM}\)
4. \(-(-\frac{12}{13})^{-4}=-(-\frac{13}{12})^{4}=-\frac{13^{4}}{12^{4}}=\text{ZRM}\left[=-\frac{28561}{20736}\right]\)
5. \((3y)^{-5}.(3y)^{-4}=(3y)^{-5+(-4)}=(3y)^{-9}=(\frac{1}{3}\frac{1}{y})^{9}\left[=\frac{1}{19683} \frac{1}{y^{9}}\right]=\text{ZRM}\)
6. \((\frac{4}{5}x)^{-4}.(\frac{4}{5}x)^{9}=(\frac{4}{5}x)^{-4+9}=(\frac{4}{5}x)^{5}\left[=\frac{1024}{3125}x^{5}\right]=\text{ZRM}\)
7. \((\frac{7}{6})^{-5}.(\frac{19}{17})^{-5}=(\frac{7}{6}\frac{19}{17})^{-5}=(\frac{133}{102})^{-5}=(\frac{102}{133})^{5}=\text{ZRM}=\left[\frac{11040808032}{41615795893}\right]\)
8. \((-\frac{16}{11})^{-1}=(-\frac{11}{16})^{1}=-\frac{11^{1}}{16^{1}}= \left[=-\frac{11}{16}\right]\)
9. \((\frac{19}{5}y)^{1}.(\frac{19}{5}y)^{-3}=(\frac{19}{5}y)^{1+(-3)}=(\frac{19}{5}y)^{-2}=(\frac{5}{19}\frac{1}{y})^{2}\left[=\frac{25}{361} \frac{1}{y^{2}}\right]\)
10. \((20c)^{-1}.(20c)^{-9}=(20c)^{-1+(-9)}=(20c)^{-10}=(\frac{1}{20}\frac{1}{c})^{10}\left[=\frac{1}{10240000000000} \frac{1}{c^{10}}\right]=\text{ZRM}\)
11. \((8c^{4})^{2}=(8)^{2}.(c^{4})^{2}=\text{ZRM}\left[=64c^{8}\right]\)
12. \((\frac{8}{7}b)^{-9}:(\frac{8}{7}b)^{-1}=(\frac{8}{7}b)^{-9-(-1)}=(\frac{8}{7}b)^{-8}=(\frac{7}{8}\frac{1}{b})^{8}=\text{ZRM}\left[ =\frac{5764801}{16777216} \frac{1}{b^{8}} \right]\)