Rekenregels machten

Hoofdmenu Eentje per keer  🖨

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

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

---

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

Verbetersleutel

1. \((-6x^{2})^{-6}=(-6)^{-6}.(x^{2})^{-6}=(\frac{1}{-6})^{6}.(\frac{1}{x^{2}})^{6}=\text{ZRM}\left[=\frac{1}{46656} \frac{1}{x^{12}}\right]\)
2. \((\frac{4}{3}b)^{4}:(\frac{4}{3}b)^{7}=(\frac{4}{3}b)^{4-7}=(\frac{4}{3}b)^{-3}=(\frac{3}{4}\frac{1}{b})^{3}=\text{ZRM}\left[ =\frac{27}{64} \frac{1}{b^{3}} \right]\)
3. \((-4y^{10})^{9}=(-4)^{9}.(y^{10})^{9}=\text{ZRM}\left[=(-262144)y^{90}\right]\)
4. \((2c)^{-4}.(2c)^{-6}=(2c)^{-4+(-6)}=(2c)^{-10}=(\frac{1}{2}\frac{1}{c})^{10}\left[=\frac{1}{1024} \frac{1}{c^{10}}\right]=\text{ZRM}\)
5. \(-(-\frac{13}{4})^{-4}=-(-\frac{4}{13})^{4}=-\frac{4^{4}}{13^{4}}=\text{ZRM}\left[=-\frac{256}{28561}\right]\)
6. \((-\frac{6}{5})^{-1}=(-\frac{5}{6})^{1}=-\frac{5^{1}}{6^{1}}= \left[=-\frac{5}{6}\right]\)
7. \((\frac{10}{11})^{-8}.(\frac{2}{19})^{-8}=(\frac{10}{11}\frac{2}{19})^{-8}=(\frac{20}{209})^{-8}=(\frac{209}{20})^{8}=\text{ZRM}=\left[\frac{3640577568861717121}{25600000000}\right]\)
8. \(-(-2)^{-5}=-(-\frac{1}{2})^{5}=+\frac{1^{5}}{2^{5}}=\text{ZRM}\left[=\frac{1}{32}\right]\)
9. \((\frac{20}{19})^{6}.(\frac{13}{7})^{6}=(\frac{20}{19}\frac{13}{7})^{6}=(\frac{260}{133})^{6}=\text{ZRM}=\left[\frac{308915776000000}{5534900853769}\right]\)
10. \((-9a^{8})^{4}=(-9)^{4}.(a^{8})^{4}=\text{ZRM}\left[=6561a^{32}\right]\)
11. \((\frac{13}{9})^{-2}.(\frac{4}{19})^{-2}=(\frac{13}{9}\frac{4}{19})^{-2}=(\frac{52}{171})^{-2}=(\frac{171}{52})^{2}=\left[\frac{29241}{2704}\right]\)
12. \(-(-\frac{20}{7})^{-2}=-(-\frac{7}{20})^{2}=-\frac{7^{2}}{20^{2}}\left[=-\frac{49}{400}\right]\)