Rekenregels machten

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

1. \((\frac{7}{5}b)^{-4}:(\frac{7}{5}b)^{4}\)
2. \((-14a^{6})^{5}\)
3. \((3c)^{-6}.(3c)^{3}\)
4. \((2x)^{-8}.(2x)^{4}\)
5. \(-(-\frac{9}{2})^{-4}\)
6. \((8c)^{-6}.(8c)^{-7}\)
7. \((5c)^{10}:(5c)^{-4}\)
8. \((\frac{11}{9}x)^{-7}:(\frac{11}{9}x)^{3}\)
9. \((2x^{8})^{3}\)
10. \((\frac{11}{19}c)^{-2}:(\frac{11}{19}c)^{-7}\)
11. \((\frac{3}{13}x)^{10}:(\frac{3}{13}x)^{8}\)
12. \((-8)^{-3}\)

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

Verbetersleutel

1. \((\frac{7}{5}b)^{-4}:(\frac{7}{5}b)^{4}=(\frac{7}{5}b)^{-4-4}=(\frac{7}{5}b)^{-8}=(\frac{5}{7}\frac{1}{b})^{8}=\text{ZRM}\left[ =\frac{390625}{5764801} \frac{1}{b^{8}} \right]\)
2. \((-14a^{6})^{5}=(-14)^{5}.(a^{6})^{5}=\text{ZRM}\left[=(-537824)a^{30}\right]\)
3. \((3c)^{-6}.(3c)^{3}=(3c)^{-6+3}=(3c)^{-3}=(\frac{1}{3}\frac{1}{c})^{3}\left[=\frac{1}{27} \frac{1}{c^{3}}\right]=\text{ZRM}\)
4. \((2x)^{-8}.(2x)^{4}=(2x)^{-8+4}=(2x)^{-4}=(\frac{1}{2}\frac{1}{x})^{4}\left[=\frac{1}{16} \frac{1}{x^{4}}\right]=\text{ZRM}\)
5. \(-(-\frac{9}{2})^{-4}=-(-\frac{2}{9})^{4}=-\frac{2^{4}}{9^{4}}=\text{ZRM}\left[=-\frac{16}{6561}\right]\)
6. \((8c)^{-6}.(8c)^{-7}=(8c)^{-6+(-7)}=(8c)^{-13}=(\frac{1}{8}\frac{1}{c})^{13}\left[=\frac{1}{549755813888} \frac{1}{c^{13}}\right]=\text{ZRM}\)
7. \((5c)^{10}:(5c)^{-4}=(5c)^{10-(-4)}=(5c)^{14}=\text{ZRM}\left[ =6103515625c^{14} \right]\)
8. \((\frac{11}{9}x)^{-7}:(\frac{11}{9}x)^{3}=(\frac{11}{9}x)^{-7-3}=(\frac{11}{9}x)^{-10}=(\frac{9}{11}\frac{1}{x})^{10}=\text{ZRM}\left[ =\frac{3486784401}{25937424601} \frac{1}{x^{10}} \right]\)
9. \((2x^{8})^{3}=(2)^{3}.(x^{8})^{3}=\text{ZRM}\left[=8x^{24}\right]\)
10. \((\frac{11}{19}c)^{-2}:(\frac{11}{19}c)^{-7}=(\frac{11}{19}c)^{-2-(-7)}=(\frac{11}{19}c)^{5}=\text{ZRM}\left[ =\frac{161051}{2476099}c^{5} \right]\)
11. \((\frac{3}{13}x)^{10}:(\frac{3}{13}x)^{8}=(\frac{3}{13}x)^{10-8}=(\frac{3}{13}x)^{2}\left[ =\frac{9}{169}x^{2} \right]\)
12. \((-8)^{-3}=(-\frac{1}{8})^{3}=-\frac{1^{3}}{8^{3}}=\text{ZRM}= \left[=-\frac{1}{512}\right]\)