Rekenregels machten

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

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

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

Verbetersleutel

1. \((5y^{5})^{7}=(5)^{7}.(y^{5})^{7}=\text{ZRM}\left[=78125y^{35}\right]\)
2. \((-\frac{11}{10})^{-6}=(-\frac{10}{11})^{6}=+\frac{10^{6}}{11^{6}}=\text{ZRM}= \left[=\frac{1000000}{1771561}\right]\)
3. \((\frac{17}{20})^{9}.(\frac{2}{5})^{9}=(\frac{17}{20}\frac{2}{5})^{9}=(\frac{17}{50})^{9}=\text{ZRM}=\left[\frac{118587876497}{1953125000000000}\right]\)
4. \((-\frac{2}{5})^{-3}=(-\frac{5}{2})^{3}=-\frac{5^{3}}{2^{3}}=\text{ZRM}= \left[=-\frac{125}{8}\right]\)
5. \((\frac{12}{17})^{10}.(\frac{3}{2})^{10}=(\frac{12}{17}\frac{3}{2})^{10}=(\frac{18}{17})^{10}=\text{ZRM}=\left[\frac{3570467226624}{2015993900449}\right]\)
6. \((\frac{5}{3}x)^{6}:(\frac{5}{3}x)^{1}=(\frac{5}{3}x)^{6-1}=(\frac{5}{3}x)^{5}=\text{ZRM}\left[ =\frac{3125}{243}x^{5} \right]\)
7. \((\frac{3}{2}c)^{-8}:(\frac{3}{2}c)^{9}=(\frac{3}{2}c)^{-8-9}=(\frac{3}{2}c)^{-17}=(\frac{2}{3}\frac{1}{c})^{17}=\text{ZRM}\left[ =\frac{131072}{129140163} \frac{1}{c^{17}} \right]\)
8. \((6c^{7})^{8}=(6)^{8}.(c^{7})^{8}=\text{ZRM}\left[=1679616c^{56}\right]\)
9. \((\frac{11}{6})^{1}.(2)^{1}=(\frac{11}{6}2)^{1}=(\frac{11}{3})^{1}=\left[\frac{11}{3}\right]\)
10. \((\frac{4}{17}y)^{1}:(\frac{4}{17}y)^{-2}=(\frac{4}{17}y)^{1-(-2)}=(\frac{4}{17}y)^{3}=\text{ZRM}\left[ =\frac{64}{4913}y^{3} \right]\)
11. \((\frac{2}{7}y)^{6}.(\frac{2}{7}y)^{-7}=(\frac{2}{7}y)^{6+(-7)}=(\frac{2}{7}y)^{-1}=(\frac{7}{2}\frac{1}{y})^{1}\left[=\frac{7}{2} \frac{1}{y^{1}}\right]\)
12. \((4y)^{-10}:(4y)^{-9}=(4y)^{-10-(-9)}=(4y)^{-1}=(\frac{1}{4}\frac{1}{y})^{1}\left[ =\frac{1}{4} \frac{1}{y^{1}} \right]\)