Rekenregels machten

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

1. \((7c^{6})^{7}\)
2. \(-(-\frac{8}{9})^{-1}\)
3. \((\frac{20}{17})^{-6}.(\frac{3}{5})^{-6}\)
4. \((\frac{17}{14}a)^{5}:(\frac{17}{14}a)^{-3}\)
5. \((\frac{19}{10})^{-8}.(3)^{-8}\)
6. \((\frac{13}{5})^{-6}.(\frac{9}{5})^{-6}\)
7. \((\frac{10}{17}c)^{6}.(\frac{10}{17}c)^{4}\)
8. \((\frac{17}{4}a)^{-1}.(\frac{17}{4}a)^{2}\)
9. \((\frac{13}{3})^{-8}.(\frac{2}{3})^{-8}\)
10. \((\frac{15}{13})^{-6}.(\frac{15}{13})^{-6}\)
11. \((\frac{12}{19})^{9}.(2)^{9}\)
12. \((-16y^{7})^{7}\)

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

Verbetersleutel

1. \((7c^{6})^{7}=(7)^{7}.(c^{6})^{7}=\text{ZRM}\left[=823543c^{42}\right]\)
2. \(-(-\frac{8}{9})^{-1}=-(-\frac{9}{8})^{1}=+\frac{9^{1}}{8^{1}}\left[=\frac{9}{8}\right]\)
3. \((\frac{20}{17})^{-6}.(\frac{3}{5})^{-6}=(\frac{20}{17}\frac{3}{5})^{-6}=(\frac{12}{17})^{-6}=(\frac{17}{12})^{6}=\text{ZRM}=\left[\frac{24137569}{2985984}\right]\)
4. \((\frac{17}{14}a)^{5}:(\frac{17}{14}a)^{-3}=(\frac{17}{14}a)^{5-(-3)}=(\frac{17}{14}a)^{8}=\text{ZRM}\left[ =\frac{6975757441}{1475789056}a^{8} \right]\)
5. \((\frac{19}{10})^{-8}.(3)^{-8}=(\frac{19}{10}3)^{-8}=(\frac{57}{10})^{-8}=(\frac{10}{57})^{8}=\text{ZRM}=\left[\frac{100000000}{111429157112001}\right]\)
6. \((\frac{13}{5})^{-6}.(\frac{9}{5})^{-6}=(\frac{13}{5}\frac{9}{5})^{-6}=(\frac{117}{25})^{-6}=(\frac{25}{117})^{6}=\text{ZRM}=\left[\frac{244140625}{2565164201769}\right]\)
7. \((\frac{10}{17}c)^{6}.(\frac{10}{17}c)^{4}=(\frac{10}{17}c)^{6+4}=(\frac{10}{17}c)^{10}\left[=\frac{10000000000}{2015993900449}c^{10}\right]=\text{ZRM}\)
8. \((\frac{17}{4}a)^{-1}.(\frac{17}{4}a)^{2}=(\frac{17}{4}a)^{-1+2}=(\frac{17}{4}a)^{1}\left[=\frac{17}{4}a^{1}\right]\)
9. \((\frac{13}{3})^{-8}.(\frac{2}{3})^{-8}=(\frac{13}{3}\frac{2}{3})^{-8}=(\frac{26}{9})^{-8}=(\frac{9}{26})^{8}=\text{ZRM}=\left[\frac{43046721}{208827064576}\right]\)
10. \((\frac{15}{13})^{-6}.(\frac{15}{13})^{-6}=(\frac{15}{13}\frac{15}{13})^{-6}=(\frac{225}{169})^{-6}=(\frac{169}{225})^{6}=\text{ZRM}=\left[\frac{23298085122481}{129746337890625}\right]\)
11. \((\frac{12}{19})^{9}.(2)^{9}=(\frac{12}{19}2)^{9}=(\frac{24}{19})^{9}=\text{ZRM}=\left[\frac{2641807540224}{322687697779}\right]\)
12. \((-16y^{7})^{7}=(-16)^{7}.(y^{7})^{7}=\text{ZRM}\left[=(-268435456)y^{49}\right]\)