Rekenregels machten

Hoofdmenu Eentje per keer  🖨

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

1. \((\frac{11}{7}y)^{6}:(\frac{11}{7}y)^{-5}\)
2. \((\frac{6}{13}x)^{-2}.(\frac{6}{13}x)^{-2}\)
3. \((\frac{3}{20}x)^{-1}.(\frac{3}{20}x)^{2}\)
4. \((\frac{5}{4}c)^{-8}.(\frac{5}{4}c)^{4}\)
5. \((-15a^{10})^{-6}\)
6. \((\frac{16}{5})^{9}.(\frac{5}{2})^{9}\)
7. \((\frac{14}{11})^{-2}.(\frac{5}{9})^{-2}\)
8. \(-(-7)^{-2}\)
9. \((-3a^{5})^{-2}\)
10. \((-5y^{3})^{-2}\)
11. \(-(-\frac{2}{13})^{-4}\)
12. \((\frac{11}{14})^{7}.(\frac{20}{3})^{7}\)

---

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

Verbetersleutel

1. \((\frac{11}{7}y)^{6}:(\frac{11}{7}y)^{-5}=(\frac{11}{7}y)^{6-(-5)}=(\frac{11}{7}y)^{11}=\text{ZRM}\left[ =\frac{285311670611}{1977326743}y^{11} \right]\)
2. \((\frac{6}{13}x)^{-2}.(\frac{6}{13}x)^{-2}=(\frac{6}{13}x)^{-2+(-2)}=(\frac{6}{13}x)^{-4}=(\frac{13}{6}\frac{1}{x})^{4}\left[=\frac{28561}{1296} \frac{1}{x^{4}}\right]=\text{ZRM}\)
3. \((\frac{3}{20}x)^{-1}.(\frac{3}{20}x)^{2}=(\frac{3}{20}x)^{-1+2}=(\frac{3}{20}x)^{1}\left[=\frac{3}{20}x^{1}\right]\)
4. \((\frac{5}{4}c)^{-8}.(\frac{5}{4}c)^{4}=(\frac{5}{4}c)^{-8+4}=(\frac{5}{4}c)^{-4}=(\frac{4}{5}\frac{1}{c})^{4}\left[=\frac{256}{625} \frac{1}{c^{4}}\right]=\text{ZRM}\)
5. \((-15a^{10})^{-6}=(-15)^{-6}.(a^{10})^{-6}=(\frac{1}{-15})^{6}.(\frac{1}{a^{10}})^{6}=\text{ZRM}\left[=\frac{1}{11390625} \frac{1}{a^{60}}\right]\)
6. \((\frac{16}{5})^{9}.(\frac{5}{2})^{9}=(\frac{16}{5}\frac{5}{2})^{9}=(8)^{9}=\text{ZRM}=\left[134217728\right]\)
7. \((\frac{14}{11})^{-2}.(\frac{5}{9})^{-2}=(\frac{14}{11}\frac{5}{9})^{-2}=(\frac{70}{99})^{-2}=(\frac{99}{70})^{2}=\left[\frac{9801}{4900}\right]\)
8. \(-(-7)^{-2}=-(-\frac{1}{7})^{2}=-\frac{1^{2}}{7^{2}}\left[=-\frac{1}{49}\right]\)
9. \((-3a^{5})^{-2}=(-3)^{-2}.(a^{5})^{-2}=(\frac{1}{-3})^{2}.(\frac{1}{a^{5}})^{2}=\text{ZRM}\left[=\frac{1}{9} \frac{1}{a^{10}}\right]\)
10. \((-5y^{3})^{-2}=(-5)^{-2}.(y^{3})^{-2}=(\frac{1}{-5})^{2}.(\frac{1}{y^{3}})^{2}=\text{ZRM}\left[=\frac{1}{25} \frac{1}{y^{6}}\right]\)
11. \(-(-\frac{2}{13})^{-4}=-(-\frac{13}{2})^{4}=-\frac{13^{4}}{2^{4}}=\text{ZRM}\left[=-\frac{28561}{16}\right]\)
12. \((\frac{11}{14})^{7}.(\frac{20}{3})^{7}=(\frac{11}{14}\frac{20}{3})^{7}=(\frac{110}{21})^{7}=\text{ZRM}=\left[\frac{194871710000000}{1801088541}\right]\)