Rekenregels machten

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

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

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

Verbetersleutel

1. \((-2)^{-2}=(-\frac{1}{2})^{2}=+\frac{1^{2}}{2^{2}}= \left[=\frac{1}{4}\right]\)
2. \((-11a^{10})^{-8}=(-11)^{-8}.(a^{10})^{-8}=(\frac{1}{-11})^{8}.(\frac{1}{a^{10}})^{8}=\text{ZRM}\left[=\frac{1}{214358881} \frac{1}{a^{80}}\right]\)
3. \((\frac{5}{4}x)^{10}:(\frac{5}{4}x)^{3}=(\frac{5}{4}x)^{10-3}=(\frac{5}{4}x)^{7}=\text{ZRM}\left[ =\frac{78125}{16384}x^{7} \right]\)
4. \((-5a^{7})^{6}=(-5)^{6}.(a^{7})^{6}=\text{ZRM}\left[=15625a^{42}\right]\)
5. \((-\frac{17}{11})^{-3}=(-\frac{11}{17})^{3}=-\frac{11^{3}}{17^{3}}=\text{ZRM}= \left[=-\frac{1331}{4913}\right]\)
6. \((\frac{15}{13}b)^{-3}.(\frac{15}{13}b)^{6}=(\frac{15}{13}b)^{-3+6}=(\frac{15}{13}b)^{3}\left[=\frac{3375}{2197}b^{3}\right]=\text{ZRM}\)
7. \(-(-\frac{19}{3})^{-5}=-(-\frac{3}{19})^{5}=+\frac{3^{5}}{19^{5}}=\text{ZRM}\left[=\frac{243}{2476099}\right]\)
8. \((\frac{4}{3})^{-2}.(2)^{-2}=(\frac{4}{3}2)^{-2}=(\frac{8}{3})^{-2}=(\frac{3}{8})^{2}=\left[\frac{9}{64}\right]\)
9. \(-(-\frac{12}{13})^{-6}=-(-\frac{13}{12})^{6}=-\frac{13^{6}}{12^{6}}=\text{ZRM}\left[=-\frac{4826809}{2985984}\right]\)
10. \((\frac{20}{3})^{1}.(\frac{14}{13})^{1}=(\frac{20}{3}\frac{14}{13})^{1}=(\frac{280}{39})^{1}=\left[\frac{280}{39}\right]\)
11. \((\frac{14}{15})^{-2}.(\frac{6}{11})^{-2}=(\frac{14}{15}\frac{6}{11})^{-2}=(\frac{28}{55})^{-2}=(\frac{55}{28})^{2}=\left[\frac{3025}{784}\right]\)
12. \((3x^{5})^{10}=(3)^{10}.(x^{5})^{10}=\text{ZRM}\left[=59049x^{50}\right]\)