Rekenregels machten

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

1. \((\frac{4}{5}x)^{-1}.(\frac{4}{5}x)^{5}\)
2. \((\frac{11}{2}y)^{-10}.(\frac{11}{2}y)^{3}\)
3. \((-\frac{7}{13})^{-5}\)
4. \((3x^{9})^{9}\)
5. \((3c)^{5}.(3c)^{6}\)
6. \((\frac{18}{17}x)^{5}.(\frac{18}{17}x)^{10}\)
7. \((8y^{5})^{-10}\)
8. \((\frac{5}{19}a)^{-5}.(\frac{5}{19}a)^{6}\)
9. \((\frac{5}{9}a)^{10}:(\frac{5}{9}a)^{3}\)
10. \(-(-\frac{10}{19})^{-5}\)
11. \((\frac{20}{19}y)^{-5}.(\frac{20}{19}y)^{-8}\)
12. \((-\frac{3}{2})^{-6}\)

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

Verbetersleutel

1. \((\frac{4}{5}x)^{-1}.(\frac{4}{5}x)^{5}=(\frac{4}{5}x)^{-1+5}=(\frac{4}{5}x)^{4}\left[=\frac{256}{625}x^{4}\right]=\text{ZRM}\)
2. \((\frac{11}{2}y)^{-10}.(\frac{11}{2}y)^{3}=(\frac{11}{2}y)^{-10+3}=(\frac{11}{2}y)^{-7}=(\frac{2}{11}\frac{1}{y})^{7}\left[=\frac{128}{19487171} \frac{1}{y^{7}}\right]=\text{ZRM}\)
3. \((-\frac{7}{13})^{-5}=(-\frac{13}{7})^{5}=-\frac{13^{5}}{7^{5}}=\text{ZRM}= \left[=-\frac{371293}{16807}\right]\)
4. \((3x^{9})^{9}=(3)^{9}.(x^{9})^{9}=\text{ZRM}\left[=19683x^{81}\right]\)
5. \((3c)^{5}.(3c)^{6}=(3c)^{5+6}=(3c)^{11}\left[=177147c^{11}\right]=\text{ZRM}\)
6. \((\frac{18}{17}x)^{5}.(\frac{18}{17}x)^{10}=(\frac{18}{17}x)^{5+10}=(\frac{18}{17}x)^{15}\left[=\frac{6746640616477458432}{2862423051509815793}x^{15}\right]=\text{ZRM}\)
7. \((8y^{5})^{-10}=(8)^{-10}.(y^{5})^{-10}=(\frac{1}{8})^{10}.(\frac{1}{y^{5}})^{10}=\text{ZRM}\left[=\frac{1}{1073741824} \frac{1}{y^{50}}\right]\)
8. \((\frac{5}{19}a)^{-5}.(\frac{5}{19}a)^{6}=(\frac{5}{19}a)^{-5+6}=(\frac{5}{19}a)^{1}\left[=\frac{5}{19}a^{1}\right]\)
9. \((\frac{5}{9}a)^{10}:(\frac{5}{9}a)^{3}=(\frac{5}{9}a)^{10-3}=(\frac{5}{9}a)^{7}=\text{ZRM}\left[ =\frac{78125}{4782969}a^{7} \right]\)
10. \(-(-\frac{10}{19})^{-5}=-(-\frac{19}{10})^{5}=+\frac{19^{5}}{10^{5}}=\text{ZRM}\left[=\frac{2476099}{100000}\right]\)
11. \((\frac{20}{19}y)^{-5}.(\frac{20}{19}y)^{-8}=(\frac{20}{19}y)^{-5+(-8)}=(\frac{20}{19}y)^{-13}=(\frac{19}{20}\frac{1}{y})^{13}\left[=\frac{42052983462257059}{81920000000000000} \frac{1}{y^{13}}\right]=\text{ZRM}\)
12. \((-\frac{3}{2})^{-6}=(-\frac{2}{3})^{6}=+\frac{2^{6}}{3^{6}}=\text{ZRM}= \left[=\frac{64}{729}\right]\)