Rekenregels machten

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

1. \((\frac{2}{5})^{5}.(\frac{6}{5})^{5}\)
2. \(-(-\frac{2}{5})^{-5}\)
3. \((\frac{5}{4}a)^{-3}:(\frac{5}{4}a)^{1}\)
4. \((\frac{13}{8}a)^{3}:(\frac{13}{8}a)^{6}\)
5. \((\frac{13}{14})^{4}.(\frac{17}{18})^{4}\)
6. \((12a^{10})^{-5}\)
7. \((\frac{17}{5})^{1}.(4)^{1}\)
8. \((4b)^{-3}:(4b)^{-6}\)
9. \((-3c^{5})^{7}\)
10. \(-(-\frac{5}{9})^{-5}\)
11. \((15y^{6})^{-3}\)
12. \(-(-\frac{5}{3})^{-1}\)

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

Verbetersleutel

1. \((\frac{2}{5})^{5}.(\frac{6}{5})^{5}=(\frac{2}{5}\frac{6}{5})^{5}=(\frac{12}{25})^{5}=\text{ZRM}=\left[\frac{248832}{9765625}\right]\)
2. \(-(-\frac{2}{5})^{-5}=-(-\frac{5}{2})^{5}=+\frac{5^{5}}{2^{5}}=\text{ZRM}\left[=\frac{3125}{32}\right]\)
3. \((\frac{5}{4}a)^{-3}:(\frac{5}{4}a)^{1}=(\frac{5}{4}a)^{-3-1}=(\frac{5}{4}a)^{-4}=(\frac{4}{5}\frac{1}{a})^{4}=\text{ZRM}\left[ =\frac{256}{625} \frac{1}{a^{4}} \right]\)
4. \((\frac{13}{8}a)^{3}:(\frac{13}{8}a)^{6}=(\frac{13}{8}a)^{3-6}=(\frac{13}{8}a)^{-3}=(\frac{8}{13}\frac{1}{a})^{3}=\text{ZRM}\left[ =\frac{512}{2197} \frac{1}{a^{3}} \right]\)
5. \((\frac{13}{14})^{4}.(\frac{17}{18})^{4}=(\frac{13}{14}\frac{17}{18})^{4}=(\frac{221}{252})^{4}=\text{ZRM}=\left[\frac{2385443281}{4032758016}\right]\)
6. \((12a^{10})^{-5}=(12)^{-5}.(a^{10})^{-5}=(\frac{1}{12})^{5}.(\frac{1}{a^{10}})^{5}=\text{ZRM}\left[=\frac{1}{248832} \frac{1}{a^{50}}\right]\)
7. \((\frac{17}{5})^{1}.(4)^{1}=(\frac{17}{5}4)^{1}=(\frac{68}{5})^{1}=\left[\frac{68}{5}\right]\)
8. \((4b)^{-3}:(4b)^{-6}=(4b)^{-3-(-6)}=(4b)^{3}=\text{ZRM}\left[ =64b^{3} \right]\)
9. \((-3c^{5})^{7}=(-3)^{7}.(c^{5})^{7}=\text{ZRM}\left[=(-2187)c^{35}\right]\)
10. \(-(-\frac{5}{9})^{-5}=-(-\frac{9}{5})^{5}=+\frac{9^{5}}{5^{5}}=\text{ZRM}\left[=\frac{59049}{3125}\right]\)
11. \((15y^{6})^{-3}=(15)^{-3}.(y^{6})^{-3}=(\frac{1}{15})^{3}.(\frac{1}{y^{6}})^{3}=\text{ZRM}\left[=\frac{1}{3375} \frac{1}{y^{18}}\right]\)
12. \(-(-\frac{5}{3})^{-1}=-(-\frac{3}{5})^{1}=+\frac{3^{1}}{5^{1}}\left[=\frac{3}{5}\right]\)