Rekenregels machten

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

1. \((\frac{15}{17})^{-8}.(\frac{11}{14})^{-8}\)
2. \((16b)^{8}.(16b)^{8}\)
3. \(-(-2)^{-6}\)
4. \((-\frac{7}{3})^{-1}\)
5. \((2y)^{1}.(2y)^{-9}\)
6. \((\frac{2}{15}c)^{9}.(\frac{2}{15}c)^{2}\)
7. \((-8x^{9})^{5}\)
8. \((2a)^{1}:(2a)^{-3}\)
9. \((14a^{6})^{5}\)
10. \((-\frac{8}{17})^{-6}\)
11. \((-\frac{11}{12})^{-6}\)
12. \((\frac{19}{14})^{5}.(\frac{17}{8})^{5}\)

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

Verbetersleutel

1. \((\frac{15}{17})^{-8}.(\frac{11}{14})^{-8}=(\frac{15}{17}\frac{11}{14})^{-8}=(\frac{165}{238})^{-8}=(\frac{238}{165})^{8}=\text{ZRM}=\left[\frac{1.0294746488738E+19}{549378366500390625}\right]\)
2. \((16b)^{8}.(16b)^{8}=(16b)^{8+8}=(16b)^{16}\left[=1.844674407371E+19b^{16}\right]=\text{ZRM}\)
3. \(-(-2)^{-6}=-(-\frac{1}{2})^{6}=-\frac{1^{6}}{2^{6}}=\text{ZRM}\left[=-\frac{1}{64}\right]\)
4. \((-\frac{7}{3})^{-1}=(-\frac{3}{7})^{1}=-\frac{3^{1}}{7^{1}}= \left[=-\frac{3}{7}\right]\)
5. \((2y)^{1}.(2y)^{-9}=(2y)^{1+(-9)}=(2y)^{-8}=(\frac{1}{2}\frac{1}{y})^{8}\left[=\frac{1}{256} \frac{1}{y^{8}}\right]=\text{ZRM}\)
6. \((\frac{2}{15}c)^{9}.(\frac{2}{15}c)^{2}=(\frac{2}{15}c)^{9+2}=(\frac{2}{15}c)^{11}\left[=\frac{2048}{8649755859375}c^{11}\right]=\text{ZRM}\)
7. \((-8x^{9})^{5}=(-8)^{5}.(x^{9})^{5}=\text{ZRM}\left[=(-32768)x^{45}\right]\)
8. \((2a)^{1}:(2a)^{-3}=(2a)^{1-(-3)}=(2a)^{4}=\text{ZRM}\left[ =16a^{4} \right]\)
9. \((14a^{6})^{5}=(14)^{5}.(a^{6})^{5}=\text{ZRM}\left[=537824a^{30}\right]\)
10. \((-\frac{8}{17})^{-6}=(-\frac{17}{8})^{6}=+\frac{17^{6}}{8^{6}}=\text{ZRM}= \left[=\frac{24137569}{262144}\right]\)
11. \((-\frac{11}{12})^{-6}=(-\frac{12}{11})^{6}=+\frac{12^{6}}{11^{6}}=\text{ZRM}= \left[=\frac{2985984}{1771561}\right]\)
12. \((\frac{19}{14})^{5}.(\frac{17}{8})^{5}=(\frac{19}{14}\frac{17}{8})^{5}=(\frac{323}{112})^{5}=\text{ZRM}=\left[\frac{3515706497843}{17623416832}\right]\)