Rekenregels machten

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

1. \((-\frac{17}{5})^{-1}\)
2. \((\frac{9}{10}a)^{4}:(\frac{9}{10}a)^{2}\)
3. \((1c^{7})^{-7}\)
4. \((\frac{17}{18}a)^{9}:(\frac{17}{18}a)^{1}\)
5. \(-(-11)^{-1}\)
6. \((\frac{16}{15})^{-10}.(\frac{3}{2})^{-10}\)
7. \((\frac{7}{5})^{5}.(\frac{9}{7})^{5}\)
8. \((\frac{9}{7}a)^{8}:(\frac{9}{7}a)^{-4}\)
9. \((12y^{2})^{-8}\)
10. \((\frac{19}{16}c)^{-2}:(\frac{19}{16}c)^{-1}\)
11. \((\frac{13}{14})^{5}.(\frac{19}{13})^{5}\)
12. \((\frac{5}{2})^{-6}.(\frac{6}{5})^{-6}\)

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

Verbetersleutel

1. \((-\frac{17}{5})^{-1}=(-\frac{5}{17})^{1}=-\frac{5^{1}}{17^{1}}= \left[=-\frac{5}{17}\right]\)
2. \((\frac{9}{10}a)^{4}:(\frac{9}{10}a)^{2}=(\frac{9}{10}a)^{4-2}=(\frac{9}{10}a)^{2}\left[ =\frac{81}{100}a^{2} \right]\)
3. \((1c^{7})^{-7}=(1)^{-7}.(c^{7})^{-7}=(1)^{7}.(\frac{1}{c^{7}})^{7}=\text{ZRM}\left[=1 \frac{1}{c^{49}}\right]\)
4. \((\frac{17}{18}a)^{9}:(\frac{17}{18}a)^{1}=(\frac{17}{18}a)^{9-1}=(\frac{17}{18}a)^{8}=\text{ZRM}\left[ =\frac{6975757441}{11019960576}a^{8} \right]\)
5. \(-(-11)^{-1}=-(-\frac{1}{11})^{1}=+\frac{1^{1}}{11^{1}}\left[=\frac{1}{11}\right]\)
6. \((\frac{16}{15})^{-10}.(\frac{3}{2})^{-10}=(\frac{16}{15}\frac{3}{2})^{-10}=(\frac{8}{5})^{-10}=(\frac{5}{8})^{10}=\text{ZRM}=\left[\frac{9765625}{1073741824}\right]\)
7. \((\frac{7}{5})^{5}.(\frac{9}{7})^{5}=(\frac{7}{5}\frac{9}{7})^{5}=(\frac{9}{5})^{5}=\text{ZRM}=\left[\frac{59049}{3125}\right]\)
8. \((\frac{9}{7}a)^{8}:(\frac{9}{7}a)^{-4}=(\frac{9}{7}a)^{8-(-4)}=(\frac{9}{7}a)^{12}=\text{ZRM}\left[ =\frac{282429536481}{13841287201}a^{12} \right]\)
9. \((12y^{2})^{-8}=(12)^{-8}.(y^{2})^{-8}=(\frac{1}{12})^{8}.(\frac{1}{y^{2}})^{8}=\text{ZRM}\left[=\frac{1}{429981696} \frac{1}{y^{16}}\right]\)
10. \((\frac{19}{16}c)^{-2}:(\frac{19}{16}c)^{-1}=(\frac{19}{16}c)^{-2-(-1)}=(\frac{19}{16}c)^{-1}=(\frac{16}{19}\frac{1}{c})^{1}\left[ =\frac{16}{19} \frac{1}{c^{1}} \right]\)
11. \((\frac{13}{14})^{5}.(\frac{19}{13})^{5}=(\frac{13}{14}\frac{19}{13})^{5}=(\frac{19}{14})^{5}=\text{ZRM}=\left[\frac{2476099}{537824}\right]\)
12. \((\frac{5}{2})^{-6}.(\frac{6}{5})^{-6}=(\frac{5}{2}\frac{6}{5})^{-6}=(3)^{-6}=(\frac{1}{3})^{6}=\text{ZRM}=\left[\frac{1}{729}\right]\)