Rekenregels machten

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

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

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

Verbetersleutel

1. \((-4)^{-6}=(-\frac{1}{4})^{6}=+\frac{1^{6}}{4^{6}}=\text{ZRM}= \left[=\frac{1}{4096}\right]\)
2. \((\frac{17}{13}c)^{8}:(\frac{17}{13}c)^{8}=(\frac{17}{13}c)^{8-8}=(\frac{17}{13}c)^{0}=1c^{0}\left[= 1 \right]\)
3. \((\frac{13}{17}x)^{2}:(\frac{13}{17}x)^{-6}=(\frac{13}{17}x)^{2-(-6)}=(\frac{13}{17}x)^{8}=\text{ZRM}\left[ =\frac{815730721}{6975757441}x^{8} \right]\)
4. \((4a)^{8}:(4a)^{6}=(4a)^{8-6}=(4a)^{2}\left[ =16a^{2} \right]\)
5. \((-1a^{3})^{-10}=(-1)^{-10}.(a^{3})^{-10}=(\frac{1}{-1})^{10}.(\frac{1}{a^{3}})^{10}=\text{ZRM}\left[=1 \frac{1}{a^{30}}\right]\)
6. \((\frac{11}{18}x)^{-9}:(\frac{11}{18}x)^{-3}=(\frac{11}{18}x)^{-9-(-3)}=(\frac{11}{18}x)^{-6}=(\frac{18}{11}\frac{1}{x})^{6}=\text{ZRM}\left[ =\frac{34012224}{1771561} \frac{1}{x^{6}} \right]\)
7. \((18b^{7})^{-9}=(18)^{-9}.(b^{7})^{-9}=(\frac{1}{18})^{9}.(\frac{1}{b^{7}})^{9}=\text{ZRM}\left[=\frac{1}{198359290368} \frac{1}{b^{63}}\right]\)
8. \((-\frac{7}{8})^{-2}=(-\frac{8}{7})^{2}=+\frac{8^{2}}{7^{2}}= \left[=\frac{64}{49}\right]\)
9. \((-\frac{7}{4})^{-2}=(-\frac{4}{7})^{2}=+\frac{4^{2}}{7^{2}}= \left[=\frac{16}{49}\right]\)
10. \((\frac{5}{6}a)^{-6}.(\frac{5}{6}a)^{10}=(\frac{5}{6}a)^{-6+10}=(\frac{5}{6}a)^{4}\left[=\frac{625}{1296}a^{4}\right]=\text{ZRM}\)
11. \((-6y^{5})^{7}=(-6)^{7}.(y^{5})^{7}=\text{ZRM}\left[=(-279936)y^{35}\right]\)
12. \((13y^{6})^{-8}=(13)^{-8}.(y^{6})^{-8}=(\frac{1}{13})^{8}.(\frac{1}{y^{6}})^{8}=\text{ZRM}\left[=\frac{1}{815730721} \frac{1}{y^{48}}\right]\)