Rekenregels machten

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

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

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

Verbetersleutel

1. \((\frac{17}{6})^{8}.(\frac{15}{19})^{8}=(\frac{17}{6}\frac{15}{19})^{8}=(\frac{85}{38})^{8}=\text{ZRM}=\left[\frac{2724905250390625}{4347792138496}\right]\)
2. \((\frac{11}{17}c)^{2}.(\frac{11}{17}c)^{-9}=(\frac{11}{17}c)^{2+(-9)}=(\frac{11}{17}c)^{-7}=(\frac{17}{11}\frac{1}{c})^{7}\left[=\frac{410338673}{19487171} \frac{1}{c^{7}}\right]=\text{ZRM}\)
3. \((\frac{2}{3}y)^{6}:(\frac{2}{3}y)^{-2}=(\frac{2}{3}y)^{6-(-2)}=(\frac{2}{3}y)^{8}=\text{ZRM}\left[ =\frac{256}{6561}y^{8} \right]\)
4. \((\frac{2}{3})^{-8}.(\frac{3}{4})^{-8}=(\frac{2}{3}\frac{3}{4})^{-8}=(\frac{1}{2})^{-8}=(2)^{8}=\text{ZRM}=\left[256\right]\)
5. \(-(-\frac{3}{13})^{-3}=-(-\frac{13}{3})^{3}=+\frac{13^{3}}{3^{3}}=\text{ZRM}\left[=\frac{2197}{27}\right]\)
6. \((\frac{3}{5}a)^{7}:(\frac{3}{5}a)^{-7}=(\frac{3}{5}a)^{7-(-7)}=(\frac{3}{5}a)^{14}=\text{ZRM}\left[ =\frac{4782969}{6103515625}a^{14} \right]\)
7. \((\frac{5}{9}y)^{-2}.(\frac{5}{9}y)^{4}=(\frac{5}{9}y)^{-2+4}=(\frac{5}{9}y)^{2}\left[=\frac{25}{81}y^{2}\right]\)
8. \((\frac{3}{2}b)^{-1}:(\frac{3}{2}b)^{-9}=(\frac{3}{2}b)^{-1-(-9)}=(\frac{3}{2}b)^{8}=\text{ZRM}\left[ =\frac{6561}{256}b^{8} \right]\)
9. \(-(-7)^{-6}=-(-\frac{1}{7})^{6}=-\frac{1^{6}}{7^{6}}=\text{ZRM}\left[=-\frac{1}{117649}\right]\)
10. \((\frac{4}{3}b)^{1}:(\frac{4}{3}b)^{4}=(\frac{4}{3}b)^{1-4}=(\frac{4}{3}b)^{-3}=(\frac{3}{4}\frac{1}{b})^{3}=\text{ZRM}\left[ =\frac{27}{64} \frac{1}{b^{3}} \right]\)
11. \((-\frac{4}{11})^{-1}=(-\frac{11}{4})^{1}=-\frac{11^{1}}{4^{1}}= \left[=-\frac{11}{4}\right]\)
12. \((-18b^{9})^{5}=(-18)^{5}.(b^{9})^{5}=\text{ZRM}\left[=(-1889568)b^{45}\right]\)