Rekenregels machten

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

1. \((\frac{17}{9}a)^{9}:(\frac{17}{9}a)^{8}\)
2. \((-\frac{17}{15})^{-4}\)
3. \(-(-6)^{-6}\)
4. \((1c^{7})^{-4}\)
5. \((11x)^{9}.(11x)^{-7}\)
6. \((\frac{3}{2})^{9}.(\frac{4}{3})^{9}\)
7. \((\frac{3}{7})^{-1}.(\frac{10}{17})^{-1}\)
8. \((6c^{3})^{-5}\)
9. \((\frac{19}{8}y)^{-2}:(\frac{19}{8}y)^{1}\)
10. \((-\frac{8}{13})^{-6}\)
11. \((-\frac{15}{19})^{-1}\)
12. \((\frac{8}{13}c)^{-5}:(\frac{8}{13}c)^{-1}\)

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

Verbetersleutel

1. \((\frac{17}{9}a)^{9}:(\frac{17}{9}a)^{8}=(\frac{17}{9}a)^{9-8}=(\frac{17}{9}a)^{1}\left[ =\frac{17}{9}a^{1} \right]\)
2. \((-\frac{17}{15})^{-4}=(-\frac{15}{17})^{4}=+\frac{15^{4}}{17^{4}}=\text{ZRM}= \left[=\frac{50625}{83521}\right]\)
3. \(-(-6)^{-6}=-(-\frac{1}{6})^{6}=-\frac{1^{6}}{6^{6}}=\text{ZRM}\left[=-\frac{1}{46656}\right]\)
4. \((1c^{7})^{-4}=(1)^{-4}.(c^{7})^{-4}=(1)^{4}.(\frac{1}{c^{7}})^{4}=\text{ZRM}\left[=1 \frac{1}{c^{28}}\right]\)
5. \((11x)^{9}.(11x)^{-7}=(11x)^{9+(-7)}=(11x)^{2}\left[=121x^{2}\right]\)
6. \((\frac{3}{2})^{9}.(\frac{4}{3})^{9}=(\frac{3}{2}\frac{4}{3})^{9}=(2)^{9}=\text{ZRM}=\left[512\right]\)
7. \((\frac{3}{7})^{-1}.(\frac{10}{17})^{-1}=(\frac{3}{7}\frac{10}{17})^{-1}=(\frac{30}{119})^{-1}=(\frac{119}{30})^{1}=\left[\frac{119}{30}\right]\)
8. \((6c^{3})^{-5}=(6)^{-5}.(c^{3})^{-5}=(\frac{1}{6})^{5}.(\frac{1}{c^{3}})^{5}=\text{ZRM}\left[=\frac{1}{7776} \frac{1}{c^{15}}\right]\)
9. \((\frac{19}{8}y)^{-2}:(\frac{19}{8}y)^{1}=(\frac{19}{8}y)^{-2-1}=(\frac{19}{8}y)^{-3}=(\frac{8}{19}\frac{1}{y})^{3}=\text{ZRM}\left[ =\frac{512}{6859} \frac{1}{y^{3}} \right]\)
10. \((-\frac{8}{13})^{-6}=(-\frac{13}{8})^{6}=+\frac{13^{6}}{8^{6}}=\text{ZRM}= \left[=\frac{4826809}{262144}\right]\)
11. \((-\frac{15}{19})^{-1}=(-\frac{19}{15})^{1}=-\frac{19^{1}}{15^{1}}= \left[=-\frac{19}{15}\right]\)
12. \((\frac{8}{13}c)^{-5}:(\frac{8}{13}c)^{-1}=(\frac{8}{13}c)^{-5-(-1)}=(\frac{8}{13}c)^{-4}=(\frac{13}{8}\frac{1}{c})^{4}=\text{ZRM}\left[ =\frac{28561}{4096} \frac{1}{c^{4}} \right]\)