Rekenregels machten

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

1. \((\frac{6}{13}x)^{9}:(\frac{6}{13}x)^{-4}\)
2. \((14c^{2})^{-2}\)
3. \((-\frac{13}{8})^{-3}\)
4. \((\frac{7}{10}a)^{-3}:(\frac{7}{10}a)^{8}\)
5. \((20c^{3})^{-5}\)
6. \(-(-\frac{13}{3})^{-2}\)
7. \((\frac{18}{17}y)^{10}:(\frac{18}{17}y)^{10}\)
8. \((5)^{5}.(\frac{7}{12})^{5}\)
9. \((-12y^{4})^{8}\)
10. \((\frac{6}{5}c)^{2}:(\frac{6}{5}c)^{10}\)
11. \((\frac{18}{11})^{-5}.(\frac{11}{12})^{-5}\)
12. \((5b^{4})^{9}\)

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

Verbetersleutel

1. \((\frac{6}{13}x)^{9}:(\frac{6}{13}x)^{-4}=(\frac{6}{13}x)^{9-(-4)}=(\frac{6}{13}x)^{13}=\text{ZRM}\left[ =\frac{13060694016}{302875106592253}x^{13} \right]\)
2. \((14c^{2})^{-2}=(14)^{-2}.(c^{2})^{-2}=(\frac{1}{14})^{2}.(\frac{1}{c^{2}})^{2}=\text{ZRM}\left[=\frac{1}{196} \frac{1}{c^{4}}\right]\)
3. \((-\frac{13}{8})^{-3}=(-\frac{8}{13})^{3}=-\frac{8^{3}}{13^{3}}=\text{ZRM}= \left[=-\frac{512}{2197}\right]\)
4. \((\frac{7}{10}a)^{-3}:(\frac{7}{10}a)^{8}=(\frac{7}{10}a)^{-3-8}=(\frac{7}{10}a)^{-11}=(\frac{10}{7}\frac{1}{a})^{11}=\text{ZRM}\left[ =\frac{100000000000}{1977326743} \frac{1}{a^{11}} \right]\)
5. \((20c^{3})^{-5}=(20)^{-5}.(c^{3})^{-5}=(\frac{1}{20})^{5}.(\frac{1}{c^{3}})^{5}=\text{ZRM}\left[=\frac{1}{3200000} \frac{1}{c^{15}}\right]\)
6. \(-(-\frac{13}{3})^{-2}=-(-\frac{3}{13})^{2}=-\frac{3^{2}}{13^{2}}\left[=-\frac{9}{169}\right]\)
7. \((\frac{18}{17}y)^{10}:(\frac{18}{17}y)^{10}=(\frac{18}{17}y)^{10-10}=(\frac{18}{17}y)^{0}=1y^{0}\left[= 1 \right]\)
8. \((5)^{5}.(\frac{7}{12})^{5}=(5\frac{7}{12})^{5}=(\frac{35}{12})^{5}=\text{ZRM}=\left[\frac{52521875}{248832}\right]\)
9. \((-12y^{4})^{8}=(-12)^{8}.(y^{4})^{8}=\text{ZRM}\left[=429981696y^{32}\right]\)
10. \((\frac{6}{5}c)^{2}:(\frac{6}{5}c)^{10}=(\frac{6}{5}c)^{2-10}=(\frac{6}{5}c)^{-8}=(\frac{5}{6}\frac{1}{c})^{8}=\text{ZRM}\left[ =\frac{390625}{1679616} \frac{1}{c^{8}} \right]\)
11. \((\frac{18}{11})^{-5}.(\frac{11}{12})^{-5}=(\frac{18}{11}\frac{11}{12})^{-5}=(\frac{3}{2})^{-5}=(\frac{2}{3})^{5}=\text{ZRM}=\left[\frac{32}{243}\right]\)
12. \((5b^{4})^{9}=(5)^{9}.(b^{4})^{9}=\text{ZRM}\left[=1953125b^{36}\right]\)