Rekenregels machten

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

1. \(-(-\frac{6}{7})^{-1}\)
2. \(-(-\frac{7}{10})^{-1}\)
3. \((\frac{18}{19}b)^{10}:(\frac{18}{19}b)^{-2}\)
4. \((17x^{3})^{-3}\)
5. \((\frac{17}{19}c)^{8}:(\frac{17}{19}c)^{2}\)
6. \((-\frac{14}{15})^{-2}\)
7. \(-(-\frac{5}{9})^{-2}\)
8. \((\frac{10}{9})^{-1}.(\frac{19}{3})^{-1}\)
9. \((8y^{4})^{8}\)
10. \((-18y^{8})^{-8}\)
11. \((3)^{6}.(\frac{12}{19})^{6}\)
12. \(-(-\frac{7}{9})^{-4}\)

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

Verbetersleutel

1. \(-(-\frac{6}{7})^{-1}=-(-\frac{7}{6})^{1}=+\frac{7^{1}}{6^{1}}\left[=\frac{7}{6}\right]\)
2. \(-(-\frac{7}{10})^{-1}=-(-\frac{10}{7})^{1}=+\frac{10^{1}}{7^{1}}\left[=\frac{10}{7}\right]\)
3. \((\frac{18}{19}b)^{10}:(\frac{18}{19}b)^{-2}=(\frac{18}{19}b)^{10-(-2)}=(\frac{18}{19}b)^{12}=\text{ZRM}\left[ =\frac{1156831381426176}{2213314919066161}b^{12} \right]\)
4. \((17x^{3})^{-3}=(17)^{-3}.(x^{3})^{-3}=(\frac{1}{17})^{3}.(\frac{1}{x^{3}})^{3}=\text{ZRM}\left[=\frac{1}{4913} \frac{1}{x^{9}}\right]\)
5. \((\frac{17}{19}c)^{8}:(\frac{17}{19}c)^{2}=(\frac{17}{19}c)^{8-2}=(\frac{17}{19}c)^{6}=\text{ZRM}\left[ =\frac{24137569}{47045881}c^{6} \right]\)
6. \((-\frac{14}{15})^{-2}=(-\frac{15}{14})^{2}=+\frac{15^{2}}{14^{2}}= \left[=\frac{225}{196}\right]\)
7. \(-(-\frac{5}{9})^{-2}=-(-\frac{9}{5})^{2}=-\frac{9^{2}}{5^{2}}\left[=-\frac{81}{25}\right]\)
8. \((\frac{10}{9})^{-1}.(\frac{19}{3})^{-1}=(\frac{10}{9}\frac{19}{3})^{-1}=(\frac{190}{27})^{-1}=(\frac{27}{190})^{1}=\left[\frac{27}{190}\right]\)
9. \((8y^{4})^{8}=(8)^{8}.(y^{4})^{8}=\text{ZRM}\left[=16777216y^{32}\right]\)
10. \((-18y^{8})^{-8}=(-18)^{-8}.(y^{8})^{-8}=(\frac{1}{-18})^{8}.(\frac{1}{y^{8}})^{8}=\text{ZRM}\left[=\frac{1}{11019960576} \frac{1}{y^{64}}\right]\)
11. \((3)^{6}.(\frac{12}{19})^{6}=(3\frac{12}{19})^{6}=(\frac{36}{19})^{6}=\text{ZRM}=\left[\frac{2176782336}{47045881}\right]\)
12. \(-(-\frac{7}{9})^{-4}=-(-\frac{9}{7})^{4}=-\frac{9^{4}}{7^{4}}=\text{ZRM}\left[=-\frac{6561}{2401}\right]\)