Rekenregels machten

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

1. \(-(-\frac{20}{17})^{-1}\)
2. \((5)^{-7}.(\frac{8}{9})^{-7}\)
3. \((9x^{9})^{-2}\)
4. \((\frac{4}{5})^{1}.(\frac{17}{10})^{1}\)
5. \((\frac{17}{9}y)^{4}.(\frac{17}{9}y)^{4}\)
6. \(-(-10)^{-2}\)
7. \((5y^{2})^{-6}\)
8. \((\frac{11}{17})^{-2}.(\frac{4}{5})^{-2}\)
9. \((-15a^{3})^{-5}\)
10. \((\frac{13}{19}c)^{-7}.(\frac{13}{19}c)^{7}\)
11. \(-(-\frac{3}{14})^{-6}\)
12. \(-(-\frac{9}{5})^{-1}\)

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

Verbetersleutel

1. \(-(-\frac{20}{17})^{-1}=-(-\frac{17}{20})^{1}=+\frac{17^{1}}{20^{1}}\left[=\frac{17}{20}\right]\)
2. \((5)^{-7}.(\frac{8}{9})^{-7}=(5\frac{8}{9})^{-7}=(\frac{40}{9})^{-7}=(\frac{9}{40})^{7}=\text{ZRM}=\left[\frac{4782969}{163840000000}\right]\)
3. \((9x^{9})^{-2}=(9)^{-2}.(x^{9})^{-2}=(\frac{1}{9})^{2}.(\frac{1}{x^{9}})^{2}=\text{ZRM}\left[=\frac{1}{81} \frac{1}{x^{18}}\right]\)
4. \((\frac{4}{5})^{1}.(\frac{17}{10})^{1}=(\frac{4}{5}\frac{17}{10})^{1}=(\frac{34}{25})^{1}=\left[\frac{34}{25}\right]\)
5. \((\frac{17}{9}y)^{4}.(\frac{17}{9}y)^{4}=(\frac{17}{9}y)^{4+4}=(\frac{17}{9}y)^{8}\left[=\frac{6975757441}{43046721}y^{8}\right]=\text{ZRM}\)
6. \(-(-10)^{-2}=-(-\frac{1}{10})^{2}=-\frac{1^{2}}{10^{2}}\left[=-\frac{1}{100}\right]\)
7. \((5y^{2})^{-6}=(5)^{-6}.(y^{2})^{-6}=(\frac{1}{5})^{6}.(\frac{1}{y^{2}})^{6}=\text{ZRM}\left[=\frac{1}{15625} \frac{1}{y^{12}}\right]\)
8. \((\frac{11}{17})^{-2}.(\frac{4}{5})^{-2}=(\frac{11}{17}\frac{4}{5})^{-2}=(\frac{44}{85})^{-2}=(\frac{85}{44})^{2}=\left[\frac{7225}{1936}\right]\)
9. \((-15a^{3})^{-5}=(-15)^{-5}.(a^{3})^{-5}=(\frac{1}{-15})^{5}.(\frac{1}{a^{3}})^{5}=\text{ZRM}\left[=(\frac{1}{-759375}) \frac{1}{a^{15}}\right]\)
10. \((\frac{13}{19}c)^{-7}.(\frac{13}{19}c)^{7}=(\frac{13}{19}c)^{-7+7}=(\frac{13}{19}c)^{0}\left[=1c^{0}\right]\left[=1\right]\)
11. \(-(-\frac{3}{14})^{-6}=-(-\frac{14}{3})^{6}=-\frac{14^{6}}{3^{6}}=\text{ZRM}\left[=-\frac{7529536}{729}\right]\)
12. \(-(-\frac{9}{5})^{-1}=-(-\frac{5}{9})^{1}=+\frac{5^{1}}{9^{1}}\left[=\frac{5}{9}\right]\)