Rekenregels machten

Hoofdmenu Eentje per keer  🖨

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

1. \((11c^{7})^{-5}\)
2. \((\frac{7}{16})^{-7}.(\frac{15}{13})^{-7}\)
3. \((\frac{13}{16}c)^{9}:(\frac{13}{16}c)^{-8}\)
4. \((\frac{9}{7}b)^{2}.(\frac{9}{7}b)^{-6}\)
5. \((-4c^{6})^{-2}\)
6. \((10y)^{9}.(10y)^{-3}\)
7. \((\frac{9}{5}x)^{1}:(\frac{9}{5}x)^{-5}\)
8. \((\frac{17}{16})^{9}.(\frac{9}{10})^{9}\)
9. \((\frac{3}{2})^{-7}.(\frac{4}{13})^{-7}\)
10. \((\frac{5}{18})^{-7}.(\frac{14}{15})^{-7}\)
11. \((\frac{4}{3}a)^{2}:(\frac{4}{3}a)^{-4}\)
12. \(-(-4)^{-6}\)

---

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

Verbetersleutel

1. \((11c^{7})^{-5}=(11)^{-5}.(c^{7})^{-5}=(\frac{1}{11})^{5}.(\frac{1}{c^{7}})^{5}=\text{ZRM}\left[=\frac{1}{161051} \frac{1}{c^{35}}\right]\)
2. \((\frac{7}{16})^{-7}.(\frac{15}{13})^{-7}=(\frac{7}{16}\frac{15}{13})^{-7}=(\frac{105}{208})^{-7}=(\frac{208}{105})^{7}=\text{ZRM}=\left[\frac{16843926774218752}{140710042265625}\right]\)
3. \((\frac{13}{16}c)^{9}:(\frac{13}{16}c)^{-8}=(\frac{13}{16}c)^{9-(-8)}=(\frac{13}{16}c)^{17}=\text{ZRM}\left[ =\frac{8650415919381337933}{2.9514790517935E+20}c^{17} \right]\)
4. \((\frac{9}{7}b)^{2}.(\frac{9}{7}b)^{-6}=(\frac{9}{7}b)^{2+(-6)}=(\frac{9}{7}b)^{-4}=(\frac{7}{9}\frac{1}{b})^{4}\left[=\frac{2401}{6561} \frac{1}{b^{4}}\right]=\text{ZRM}\)
5. \((-4c^{6})^{-2}=(-4)^{-2}.(c^{6})^{-2}=(\frac{1}{-4})^{2}.(\frac{1}{c^{6}})^{2}=\text{ZRM}\left[=\frac{1}{16} \frac{1}{c^{12}}\right]\)
6. \((10y)^{9}.(10y)^{-3}=(10y)^{9+(-3)}=(10y)^{6}\left[=1000000y^{6}\right]=\text{ZRM}\)
7. \((\frac{9}{5}x)^{1}:(\frac{9}{5}x)^{-5}=(\frac{9}{5}x)^{1-(-5)}=(\frac{9}{5}x)^{6}=\text{ZRM}\left[ =\frac{531441}{15625}x^{6} \right]\)
8. \((\frac{17}{16})^{9}.(\frac{9}{10})^{9}=(\frac{17}{16}\frac{9}{10})^{9}=(\frac{153}{160})^{9}=\text{ZRM}=\left[\frac{4.5943373101939E+19}{6.8719476736E+19}\right]\)
9. \((\frac{3}{2})^{-7}.(\frac{4}{13})^{-7}=(\frac{3}{2}\frac{4}{13})^{-7}=(\frac{6}{13})^{-7}=(\frac{13}{6})^{7}=\text{ZRM}=\left[\frac{62748517}{279936}\right]\)
10. \((\frac{5}{18})^{-7}.(\frac{14}{15})^{-7}=(\frac{5}{18}\frac{14}{15})^{-7}=(\frac{7}{27})^{-7}=(\frac{27}{7})^{7}=\text{ZRM}=\left[\frac{10460353203}{823543}\right]\)
11. \((\frac{4}{3}a)^{2}:(\frac{4}{3}a)^{-4}=(\frac{4}{3}a)^{2-(-4)}=(\frac{4}{3}a)^{6}=\text{ZRM}\left[ =\frac{4096}{729}a^{6} \right]\)
12. \(-(-4)^{-6}=-(-\frac{1}{4})^{6}=-\frac{1^{6}}{4^{6}}=\text{ZRM}\left[=-\frac{1}{4096}\right]\)