Rekenregels machten

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

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

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

Verbetersleutel

1. \((\frac{9}{14}y)^{-4}.(\frac{9}{14}y)^{-4}=(\frac{9}{14}y)^{-4+(-4)}=(\frac{9}{14}y)^{-8}=(\frac{14}{9}\frac{1}{y})^{8}\left[=\frac{1475789056}{43046721} \frac{1}{y^{8}}\right]=\text{ZRM}\)
2. \((-15b^{8})^{-6}=(-15)^{-6}.(b^{8})^{-6}=(\frac{1}{-15})^{6}.(\frac{1}{b^{8}})^{6}=\text{ZRM}\left[=\frac{1}{11390625} \frac{1}{b^{48}}\right]\)
3. \((-\frac{4}{5})^{-1}=(-\frac{5}{4})^{1}=-\frac{5^{1}}{4^{1}}= \left[=-\frac{5}{4}\right]\)
4. \((-\frac{16}{19})^{-1}=(-\frac{19}{16})^{1}=-\frac{19^{1}}{16^{1}}= \left[=-\frac{19}{16}\right]\)
5. \((\frac{9}{11}a)^{1}.(\frac{9}{11}a)^{-1}=(\frac{9}{11}a)^{1+(-1)}=(\frac{9}{11}a)^{0}\left[=1a^{0}\right]\left[=1\right]\)
6. \((\frac{10}{3}x)^{7}.(\frac{10}{3}x)^{-9}=(\frac{10}{3}x)^{7+(-9)}=(\frac{10}{3}x)^{-2}=(\frac{3}{10}\frac{1}{x})^{2}\left[=\frac{9}{100} \frac{1}{x^{2}}\right]\)
7. \((\frac{17}{19})^{7}.(\frac{9}{7})^{7}=(\frac{17}{19}\frac{9}{7})^{7}=(\frac{153}{133})^{7}=\text{ZRM}=\left[\frac{1962637152460137}{736141813551277}\right]\)
8. \((-\frac{6}{19})^{-5}=(-\frac{19}{6})^{5}=-\frac{19^{5}}{6^{5}}=\text{ZRM}= \left[=-\frac{2476099}{7776}\right]\)
9. \((\frac{19}{3})^{-9}.(\frac{13}{19})^{-9}=(\frac{19}{3}\frac{13}{19})^{-9}=(\frac{13}{3})^{-9}=(\frac{3}{13})^{9}=\text{ZRM}=\left[\frac{19683}{10604499373}\right]\)
10. \((\frac{14}{3}y)^{2}.(\frac{14}{3}y)^{-9}=(\frac{14}{3}y)^{2+(-9)}=(\frac{14}{3}y)^{-7}=(\frac{3}{14}\frac{1}{y})^{7}\left[=\frac{2187}{105413504} \frac{1}{y^{7}}\right]=\text{ZRM}\)
11. \((-\frac{13}{8})^{-3}=(-\frac{8}{13})^{3}=-\frac{8^{3}}{13^{3}}=\text{ZRM}= \left[=-\frac{512}{2197}\right]\)
12. \(-(-\frac{7}{16})^{-5}=-(-\frac{16}{7})^{5}=+\frac{16^{5}}{7^{5}}=\text{ZRM}\left[=\frac{1048576}{16807}\right]\)