Rekenregels machten

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

1. \((-\frac{18}{17})^{-4}\)
2. \((\frac{14}{9}y)^{6}.(\frac{14}{9}y)^{-7}\)
3. \((-10)^{-2}\)
4. \((\frac{5}{3}b)^{-2}:(\frac{5}{3}b)^{-9}\)
5. \((\frac{19}{2}b)^{1}:(\frac{19}{2}b)^{-1}\)
6. \((\frac{16}{9})^{-5}.(\frac{4}{15})^{-5}\)
7. \(-(-\frac{15}{14})^{-2}\)
8. \((\frac{15}{19}x)^{3}:(\frac{15}{19}x)^{7}\)
9. \((-\frac{6}{5})^{-1}\)
10. \((\frac{12}{17})^{10}.(\frac{2}{5})^{10}\)
11. \((-\frac{5}{9})^{-4}\)
12. \((\frac{13}{8}c)^{-8}.(\frac{13}{8}c)^{1}\)

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

Verbetersleutel

1. \((-\frac{18}{17})^{-4}=(-\frac{17}{18})^{4}=+\frac{17^{4}}{18^{4}}=\text{ZRM}= \left[=\frac{83521}{104976}\right]\)
2. \((\frac{14}{9}y)^{6}.(\frac{14}{9}y)^{-7}=(\frac{14}{9}y)^{6+(-7)}=(\frac{14}{9}y)^{-1}=(\frac{9}{14}\frac{1}{y})^{1}\left[=\frac{9}{14} \frac{1}{y^{1}}\right]\)
3. \((-10)^{-2}=(-\frac{1}{10})^{2}=+\frac{1^{2}}{10^{2}}= \left[=\frac{1}{100}\right]\)
4. \((\frac{5}{3}b)^{-2}:(\frac{5}{3}b)^{-9}=(\frac{5}{3}b)^{-2-(-9)}=(\frac{5}{3}b)^{7}=\text{ZRM}\left[ =\frac{78125}{2187}b^{7} \right]\)
5. \((\frac{19}{2}b)^{1}:(\frac{19}{2}b)^{-1}=(\frac{19}{2}b)^{1-(-1)}=(\frac{19}{2}b)^{2}\left[ =\frac{361}{4}b^{2} \right]\)
6. \((\frac{16}{9})^{-5}.(\frac{4}{15})^{-5}=(\frac{16}{9}\frac{4}{15})^{-5}=(\frac{64}{135})^{-5}=(\frac{135}{64})^{5}=\text{ZRM}=\left[\frac{44840334375}{1073741824}\right]\)
7. \(-(-\frac{15}{14})^{-2}=-(-\frac{14}{15})^{2}=-\frac{14^{2}}{15^{2}}\left[=-\frac{196}{225}\right]\)
8. \((\frac{15}{19}x)^{3}:(\frac{15}{19}x)^{7}=(\frac{15}{19}x)^{3-7}=(\frac{15}{19}x)^{-4}=(\frac{19}{15}\frac{1}{x})^{4}=\text{ZRM}\left[ =\frac{130321}{50625} \frac{1}{x^{4}} \right]\)
9. \((-\frac{6}{5})^{-1}=(-\frac{5}{6})^{1}=-\frac{5^{1}}{6^{1}}= \left[=-\frac{5}{6}\right]\)
10. \((\frac{12}{17})^{10}.(\frac{2}{5})^{10}=(\frac{12}{17}\frac{2}{5})^{10}=(\frac{24}{85})^{10}=\text{ZRM}=\left[\frac{63403380965376}{1.9687440434072E+19}\right]\)
11. \((-\frac{5}{9})^{-4}=(-\frac{9}{5})^{4}=+\frac{9^{4}}{5^{4}}=\text{ZRM}= \left[=\frac{6561}{625}\right]\)
12. \((\frac{13}{8}c)^{-8}.(\frac{13}{8}c)^{1}=(\frac{13}{8}c)^{-8+1}=(\frac{13}{8}c)^{-7}=(\frac{8}{13}\frac{1}{c})^{7}\left[=\frac{2097152}{62748517} \frac{1}{c^{7}}\right]=\text{ZRM}\)