Rekenregels machten

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

1. \((\frac{19}{18}c)^{10}.(\frac{19}{18}c)^{-4}\)
2. \((14b)^{1}.(14b)^{9}\)
3. \(-(-\frac{3}{4})^{-6}\)
4. \((\frac{12}{17}y)^{-6}.(\frac{12}{17}y)^{2}\)
5. \((-\frac{9}{10})^{-1}\)
6. \((\frac{5}{16})^{10}.(2)^{10}\)
7. \((\frac{17}{5}x)^{1}.(\frac{17}{5}x)^{-3}\)
8. \((\frac{17}{19}b)^{-9}.(\frac{17}{19}b)^{-7}\)
9. \((\frac{5}{19})^{-6}.(\frac{17}{2})^{-6}\)
10. \(-(-\frac{8}{7})^{-5}\)
11. \((\frac{2}{3}a)^{7}.(\frac{2}{3}a)^{6}\)
12. \((\frac{3}{10})^{1}.(\frac{17}{20})^{1}\)

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

Verbetersleutel

1. \((\frac{19}{18}c)^{10}.(\frac{19}{18}c)^{-4}=(\frac{19}{18}c)^{10+(-4)}=(\frac{19}{18}c)^{6}\left[=\frac{47045881}{34012224}c^{6}\right]=\text{ZRM}\)
2. \((14b)^{1}.(14b)^{9}=(14b)^{1+9}=(14b)^{10}\left[=289254654976b^{10}\right]=\text{ZRM}\)
3. \(-(-\frac{3}{4})^{-6}=-(-\frac{4}{3})^{6}=-\frac{4^{6}}{3^{6}}=\text{ZRM}\left[=-\frac{4096}{729}\right]\)
4. \((\frac{12}{17}y)^{-6}.(\frac{12}{17}y)^{2}=(\frac{12}{17}y)^{-6+2}=(\frac{12}{17}y)^{-4}=(\frac{17}{12}\frac{1}{y})^{4}\left[=\frac{83521}{20736} \frac{1}{y^{4}}\right]=\text{ZRM}\)
5. \((-\frac{9}{10})^{-1}=(-\frac{10}{9})^{1}=-\frac{10^{1}}{9^{1}}= \left[=-\frac{10}{9}\right]\)
6. \((\frac{5}{16})^{10}.(2)^{10}=(\frac{5}{16}2)^{10}=(\frac{5}{8})^{10}=\text{ZRM}=\left[\frac{9765625}{1073741824}\right]\)
7. \((\frac{17}{5}x)^{1}.(\frac{17}{5}x)^{-3}=(\frac{17}{5}x)^{1+(-3)}=(\frac{17}{5}x)^{-2}=(\frac{5}{17}\frac{1}{x})^{2}\left[=\frac{25}{289} \frac{1}{x^{2}}\right]\)
8. \((\frac{17}{19}b)^{-9}.(\frac{17}{19}b)^{-7}=(\frac{17}{19}b)^{-9+(-7)}=(\frac{17}{19}b)^{-16}=(\frac{19}{17}\frac{1}{b})^{16}\left[=\frac{2.8844141356762E+20}{4.8661191875667E+19} \frac{1}{b^{16}}\right]=\text{ZRM}\)
9. \((\frac{5}{19})^{-6}.(\frac{17}{2})^{-6}=(\frac{5}{19}\frac{17}{2})^{-6}=(\frac{85}{38})^{-6}=(\frac{38}{85})^{6}=\text{ZRM}=\left[\frac{3010936384}{377149515625}\right]\)
10. \(-(-\frac{8}{7})^{-5}=-(-\frac{7}{8})^{5}=+\frac{7^{5}}{8^{5}}=\text{ZRM}\left[=\frac{16807}{32768}\right]\)
11. \((\frac{2}{3}a)^{7}.(\frac{2}{3}a)^{6}=(\frac{2}{3}a)^{7+6}=(\frac{2}{3}a)^{13}\left[=\frac{8192}{1594323}a^{13}\right]=\text{ZRM}\)
12. \((\frac{3}{10})^{1}.(\frac{17}{20})^{1}=(\frac{3}{10}\frac{17}{20})^{1}=(\frac{51}{200})^{1}=\left[\frac{51}{200}\right]\)