Rekenregels machten

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

1. \((15x^{8})^{-6}\)
2. \((\frac{17}{4}a)^{-9}.(\frac{17}{4}a)^{-3}\)
3. \((\frac{17}{18})^{2}.(\frac{7}{10})^{2}\)
4. \((20a^{6})^{10}\)
5. \((14b^{4})^{7}\)
6. \((\frac{9}{2})^{-10}.(\frac{8}{13})^{-10}\)
7. \((-7)^{-3}\)
8. \((-\frac{9}{16})^{-4}\)
9. \(-(-\frac{9}{11})^{-2}\)
10. \((11y^{8})^{2}\)
11. \((\frac{13}{9}c)^{10}.(\frac{13}{9}c)^{3}\)
12. \((\frac{7}{2}y)^{6}.(\frac{7}{2}y)^{-1}\)

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

Verbetersleutel

1. \((15x^{8})^{-6}=(15)^{-6}.(x^{8})^{-6}=(\frac{1}{15})^{6}.(\frac{1}{x^{8}})^{6}=\text{ZRM}\left[=\frac{1}{11390625} \frac{1}{x^{48}}\right]\)
2. \((\frac{17}{4}a)^{-9}.(\frac{17}{4}a)^{-3}=(\frac{17}{4}a)^{-9+(-3)}=(\frac{17}{4}a)^{-12}=(\frac{4}{17}\frac{1}{a})^{12}\left[=\frac{16777216}{582622237229761} \frac{1}{a^{12}}\right]=\text{ZRM}\)
3. \((\frac{17}{18})^{2}.(\frac{7}{10})^{2}=(\frac{17}{18}\frac{7}{10})^{2}=(\frac{119}{180})^{2}=\left[\frac{14161}{32400}\right]\)
4. \((20a^{6})^{10}=(20)^{10}.(a^{6})^{10}=\text{ZRM}\left[=10240000000000a^{60}\right]\)
5. \((14b^{4})^{7}=(14)^{7}.(b^{4})^{7}=\text{ZRM}\left[=105413504b^{28}\right]\)
6. \((\frac{9}{2})^{-10}.(\frac{8}{13})^{-10}=(\frac{9}{2}\frac{8}{13})^{-10}=(\frac{36}{13})^{-10}=(\frac{13}{36})^{10}=\text{ZRM}=\left[\frac{137858491849}{3656158440062976}\right]\)
7. \((-7)^{-3}=(-\frac{1}{7})^{3}=-\frac{1^{3}}{7^{3}}=\text{ZRM}= \left[=-\frac{1}{343}\right]\)
8. \((-\frac{9}{16})^{-4}=(-\frac{16}{9})^{4}=+\frac{16^{4}}{9^{4}}=\text{ZRM}= \left[=\frac{65536}{6561}\right]\)
9. \(-(-\frac{9}{11})^{-2}=-(-\frac{11}{9})^{2}=-\frac{11^{2}}{9^{2}}\left[=-\frac{121}{81}\right]\)
10. \((11y^{8})^{2}=(11)^{2}.(y^{8})^{2}=\text{ZRM}\left[=121y^{16}\right]\)
11. \((\frac{13}{9}c)^{10}.(\frac{13}{9}c)^{3}=(\frac{13}{9}c)^{10+3}=(\frac{13}{9}c)^{13}\left[=\frac{302875106592253}{2541865828329}c^{13}\right]=\text{ZRM}\)
12. \((\frac{7}{2}y)^{6}.(\frac{7}{2}y)^{-1}=(\frac{7}{2}y)^{6+(-1)}=(\frac{7}{2}y)^{5}\left[=\frac{16807}{32}y^{5}\right]=\text{ZRM}\)