Rekenregels machten

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

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

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

Verbetersleutel

1. \(-(-\frac{9}{5})^{-4}=-(-\frac{5}{9})^{4}=-\frac{5^{4}}{9^{4}}=\text{ZRM}\left[=-\frac{625}{6561}\right]\)
2. \(-(-\frac{5}{2})^{-3}=-(-\frac{2}{5})^{3}=+\frac{2^{3}}{5^{3}}=\text{ZRM}\left[=\frac{8}{125}\right]\)
3. \(-(-\frac{3}{2})^{-4}=-(-\frac{2}{3})^{4}=-\frac{2^{4}}{3^{4}}=\text{ZRM}\left[=-\frac{16}{81}\right]\)
4. \((-13b^{3})^{-8}=(-13)^{-8}.(b^{3})^{-8}=(\frac{1}{-13})^{8}.(\frac{1}{b^{3}})^{8}=\text{ZRM}\left[=\frac{1}{815730721} \frac{1}{b^{24}}\right]\)
5. \((-\frac{7}{6})^{-4}=(-\frac{6}{7})^{4}=+\frac{6^{4}}{7^{4}}=\text{ZRM}= \left[=\frac{1296}{2401}\right]\)
6. \((\frac{15}{13}y)^{6}:(\frac{15}{13}y)^{6}=(\frac{15}{13}y)^{6-6}=(\frac{15}{13}y)^{0}=1y^{0}\left[= 1 \right]\)
7. \((-\frac{6}{5})^{-3}=(-\frac{5}{6})^{3}=-\frac{5^{3}}{6^{3}}=\text{ZRM}= \left[=-\frac{125}{216}\right]\)
8. \((-\frac{5}{7})^{-4}=(-\frac{7}{5})^{4}=+\frac{7^{4}}{5^{4}}=\text{ZRM}= \left[=\frac{2401}{625}\right]\)
9. \((\frac{9}{4})^{-5}.(\frac{8}{3})^{-5}=(\frac{9}{4}\frac{8}{3})^{-5}=(6)^{-5}=(\frac{1}{6})^{5}=\text{ZRM}=\left[\frac{1}{7776}\right]\)
10. \((-\frac{7}{9})^{-2}=(-\frac{9}{7})^{2}=+\frac{9^{2}}{7^{2}}= \left[=\frac{81}{49}\right]\)
11. \((15c^{4})^{5}=(15)^{5}.(c^{4})^{5}=\text{ZRM}\left[=759375c^{20}\right]\)
12. \((\frac{17}{5}b)^{-9}.(\frac{17}{5}b)^{-3}=(\frac{17}{5}b)^{-9+(-3)}=(\frac{17}{5}b)^{-12}=(\frac{5}{17}\frac{1}{b})^{12}\left[=\frac{244140625}{582622237229761} \frac{1}{b^{12}}\right]=\text{ZRM}\)