Rekenregels machten

Hoofdmenu Eentje per keer  🖨

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

1. \((5x^{3})^{-2}\)
2. \(-(-2)^{-1}\)
3. \((-\frac{5}{14})^{-1}\)
4. \((\frac{4}{9}x)^{10}.(\frac{4}{9}x)^{7}\)
5. \((-\frac{12}{17})^{-1}\)
6. \((-\frac{12}{17})^{-2}\)
7. \((\frac{2}{5}c)^{-1}.(\frac{2}{5}c)^{-1}\)
8. \((\frac{4}{3})^{5}.(\frac{5}{18})^{5}\)
9. \((\frac{3}{2})^{5}.(2)^{5}\)
10. \((-\frac{19}{16})^{-5}\)
11. \((-\frac{11}{5})^{-3}\)
12. \(-(-\frac{3}{10})^{-1}\)

---

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

Verbetersleutel

1. \((5x^{3})^{-2}=(5)^{-2}.(x^{3})^{-2}=(\frac{1}{5})^{2}.(\frac{1}{x^{3}})^{2}=\text{ZRM}\left[=\frac{1}{25} \frac{1}{x^{6}}\right]\)
2. \(-(-2)^{-1}=-(-\frac{1}{2})^{1}=+\frac{1^{1}}{2^{1}}\left[=\frac{1}{2}\right]\)
3. \((-\frac{5}{14})^{-1}=(-\frac{14}{5})^{1}=-\frac{14^{1}}{5^{1}}= \left[=-\frac{14}{5}\right]\)
4. \((\frac{4}{9}x)^{10}.(\frac{4}{9}x)^{7}=(\frac{4}{9}x)^{10+7}=(\frac{4}{9}x)^{17}\left[=\frac{17179869184}{16677181699666569}x^{17}\right]=\text{ZRM}\)
5. \((-\frac{12}{17})^{-1}=(-\frac{17}{12})^{1}=-\frac{17^{1}}{12^{1}}= \left[=-\frac{17}{12}\right]\)
6. \((-\frac{12}{17})^{-2}=(-\frac{17}{12})^{2}=+\frac{17^{2}}{12^{2}}= \left[=\frac{289}{144}\right]\)
7. \((\frac{2}{5}c)^{-1}.(\frac{2}{5}c)^{-1}=(\frac{2}{5}c)^{-1+(-1)}=(\frac{2}{5}c)^{-2}=(\frac{5}{2}\frac{1}{c})^{2}\left[=\frac{25}{4} \frac{1}{c^{2}}\right]\)
8. \((\frac{4}{3})^{5}.(\frac{5}{18})^{5}=(\frac{4}{3}\frac{5}{18})^{5}=(\frac{10}{27})^{5}=\text{ZRM}=\left[\frac{100000}{14348907}\right]\)
9. \((\frac{3}{2})^{5}.(2)^{5}=(\frac{3}{2}2)^{5}=(3)^{5}=\text{ZRM}=\left[243\right]\)
10. \((-\frac{19}{16})^{-5}=(-\frac{16}{19})^{5}=-\frac{16^{5}}{19^{5}}=\text{ZRM}= \left[=-\frac{1048576}{2476099}\right]\)
11. \((-\frac{11}{5})^{-3}=(-\frac{5}{11})^{3}=-\frac{5^{3}}{11^{3}}=\text{ZRM}= \left[=-\frac{125}{1331}\right]\)
12. \(-(-\frac{3}{10})^{-1}=-(-\frac{10}{3})^{1}=+\frac{10^{1}}{3^{1}}\left[=\frac{10}{3}\right]\)