Rekenregels machten

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

1. \((10y)^{1}.(10y)^{10}\)
2. \((20x^{2})^{-10}\)
3. \(-(-\frac{17}{20})^{-1}\)
4. \((\frac{5}{16}c)^{-3}:(\frac{5}{16}c)^{7}\)
5. \((\frac{7}{5})^{-6}.(\frac{10}{19})^{-6}\)
6. \((-\frac{13}{10})^{-4}\)
7. \((\frac{3}{11})^{7}.(\frac{10}{9})^{7}\)
8. \((\frac{14}{11}y)^{-6}:(\frac{14}{11}y)^{1}\)
9. \(-(-\frac{3}{17})^{-3}\)
10. \((\frac{4}{3}a)^{-4}:(\frac{4}{3}a)^{-7}\)
11. \((14y)^{2}.(14y)^{3}\)
12. \((\frac{14}{3}b)^{-5}:(\frac{14}{3}b)^{-10}\)

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

Verbetersleutel

1. \((10y)^{1}.(10y)^{10}=(10y)^{1+10}=(10y)^{11}\left[=100000000000y^{11}\right]=\text{ZRM}\)
2. \((20x^{2})^{-10}=(20)^{-10}.(x^{2})^{-10}=(\frac{1}{20})^{10}.(\frac{1}{x^{2}})^{10}=\text{ZRM}\left[=\frac{1}{10240000000000} \frac{1}{x^{20}}\right]\)
3. \(-(-\frac{17}{20})^{-1}=-(-\frac{20}{17})^{1}=+\frac{20^{1}}{17^{1}}\left[=\frac{20}{17}\right]\)
4. \((\frac{5}{16}c)^{-3}:(\frac{5}{16}c)^{7}=(\frac{5}{16}c)^{-3-7}=(\frac{5}{16}c)^{-10}=(\frac{16}{5}\frac{1}{c})^{10}=\text{ZRM}\left[ =\frac{1099511627776}{9765625} \frac{1}{c^{10}} \right]\)
5. \((\frac{7}{5})^{-6}.(\frac{10}{19})^{-6}=(\frac{7}{5}\frac{10}{19})^{-6}=(\frac{14}{19})^{-6}=(\frac{19}{14})^{6}=\text{ZRM}=\left[\frac{47045881}{7529536}\right]\)
6. \((-\frac{13}{10})^{-4}=(-\frac{10}{13})^{4}=+\frac{10^{4}}{13^{4}}=\text{ZRM}= \left[=\frac{10000}{28561}\right]\)
7. \((\frac{3}{11})^{7}.(\frac{10}{9})^{7}=(\frac{3}{11}\frac{10}{9})^{7}=(\frac{10}{33})^{7}=\text{ZRM}=\left[\frac{10000000}{42618442977}\right]\)
8. \((\frac{14}{11}y)^{-6}:(\frac{14}{11}y)^{1}=(\frac{14}{11}y)^{-6-1}=(\frac{14}{11}y)^{-7}=(\frac{11}{14}\frac{1}{y})^{7}=\text{ZRM}\left[ =\frac{19487171}{105413504} \frac{1}{y^{7}} \right]\)
9. \(-(-\frac{3}{17})^{-3}=-(-\frac{17}{3})^{3}=+\frac{17^{3}}{3^{3}}=\text{ZRM}\left[=\frac{4913}{27}\right]\)
10. \((\frac{4}{3}a)^{-4}:(\frac{4}{3}a)^{-7}=(\frac{4}{3}a)^{-4-(-7)}=(\frac{4}{3}a)^{3}=\text{ZRM}\left[ =\frac{64}{27}a^{3} \right]\)
11. \((14y)^{2}.(14y)^{3}=(14y)^{2+3}=(14y)^{5}\left[=537824y^{5}\right]=\text{ZRM}\)
12. \((\frac{14}{3}b)^{-5}:(\frac{14}{3}b)^{-10}=(\frac{14}{3}b)^{-5-(-10)}=(\frac{14}{3}b)^{5}=\text{ZRM}\left[ =\frac{537824}{243}b^{5} \right]\)