Rekenregels machten

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

1. \((19x^{4})^{-8}\)
2. \((20y^{4})^{-5}\)
3. \(-(-\frac{8}{17})^{-4}\)
4. \((\frac{9}{16})^{5}.(\frac{2}{19})^{5}\)
5. \(-(-\frac{6}{5})^{-6}\)
6. \((\frac{9}{5})^{-9}.(\frac{4}{13})^{-9}\)
7. \((\frac{5}{7}y)^{9}.(\frac{5}{7}y)^{-9}\)
8. \(-(-9)^{-3}\)
9. \((-4a^{9})^{3}\)
10. \((-20a^{5})^{-2}\)
11. \((\frac{17}{11})^{1}.(\frac{3}{4})^{1}\)
12. \((-\frac{17}{11})^{-5}\)

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

Verbetersleutel

1. \((19x^{4})^{-8}=(19)^{-8}.(x^{4})^{-8}=(\frac{1}{19})^{8}.(\frac{1}{x^{4}})^{8}=\text{ZRM}\left[=\frac{1}{16983563041} \frac{1}{x^{32}}\right]\)
2. \((20y^{4})^{-5}=(20)^{-5}.(y^{4})^{-5}=(\frac{1}{20})^{5}.(\frac{1}{y^{4}})^{5}=\text{ZRM}\left[=\frac{1}{3200000} \frac{1}{y^{20}}\right]\)
3. \(-(-\frac{8}{17})^{-4}=-(-\frac{17}{8})^{4}=-\frac{17^{4}}{8^{4}}=\text{ZRM}\left[=-\frac{83521}{4096}\right]\)
4. \((\frac{9}{16})^{5}.(\frac{2}{19})^{5}=(\frac{9}{16}\frac{2}{19})^{5}=(\frac{9}{152})^{5}=\text{ZRM}=\left[\frac{59049}{81136812032}\right]\)
5. \(-(-\frac{6}{5})^{-6}=-(-\frac{5}{6})^{6}=-\frac{5^{6}}{6^{6}}=\text{ZRM}\left[=-\frac{15625}{46656}\right]\)
6. \((\frac{9}{5})^{-9}.(\frac{4}{13})^{-9}=(\frac{9}{5}\frac{4}{13})^{-9}=(\frac{36}{65})^{-9}=(\frac{65}{36})^{9}=\text{ZRM}=\left[\frac{20711912837890625}{101559956668416}\right]\)
7. \((\frac{5}{7}y)^{9}.(\frac{5}{7}y)^{-9}=(\frac{5}{7}y)^{9+(-9)}=(\frac{5}{7}y)^{0}\left[=1y^{0}\right]\left[=1\right]\)
8. \(-(-9)^{-3}=-(-\frac{1}{9})^{3}=+\frac{1^{3}}{9^{3}}=\text{ZRM}\left[=\frac{1}{729}\right]\)
9. \((-4a^{9})^{3}=(-4)^{3}.(a^{9})^{3}=\text{ZRM}\left[=(-64)a^{27}\right]\)
10. \((-20a^{5})^{-2}=(-20)^{-2}.(a^{5})^{-2}=(\frac{1}{-20})^{2}.(\frac{1}{a^{5}})^{2}=\text{ZRM}\left[=\frac{1}{400} \frac{1}{a^{10}}\right]\)
11. \((\frac{17}{11})^{1}.(\frac{3}{4})^{1}=(\frac{17}{11}\frac{3}{4})^{1}=(\frac{51}{44})^{1}=\left[\frac{51}{44}\right]\)
12. \((-\frac{17}{11})^{-5}=(-\frac{11}{17})^{5}=-\frac{11^{5}}{17^{5}}=\text{ZRM}= \left[=-\frac{161051}{1419857}\right]\)