Rekenregels machten

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

1. \((2b)^{8}:(2b)^{-8}\)
2. \((\frac{6}{17}c)^{-7}.(\frac{6}{17}c)^{-3}\)
3. \((4x)^{-3}.(4x)^{-8}\)
4. \((\frac{16}{3}c)^{-3}:(\frac{16}{3}c)^{-5}\)
5. \((\frac{7}{4})^{2}.(2)^{2}\)
6. \((-\frac{9}{20})^{-2}\)
7. \((\frac{5}{8}c)^{4}.(\frac{5}{8}c)^{9}\)
8. \((-\frac{3}{10})^{-6}\)
9. \((\frac{17}{5}a)^{-4}:(\frac{17}{5}a)^{5}\)
10. \((-\frac{13}{14})^{-6}\)
11. \((\frac{18}{17}y)^{6}.(\frac{18}{17}y)^{-10}\)
12. \((-\frac{9}{20})^{-3}\)

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

Verbetersleutel

1. \((2b)^{8}:(2b)^{-8}=(2b)^{8-(-8)}=(2b)^{16}=\text{ZRM}\left[ =65536b^{16} \right]\)
2. \((\frac{6}{17}c)^{-7}.(\frac{6}{17}c)^{-3}=(\frac{6}{17}c)^{-7+(-3)}=(\frac{6}{17}c)^{-10}=(\frac{17}{6}\frac{1}{c})^{10}\left[=\frac{2015993900449}{60466176} \frac{1}{c^{10}}\right]=\text{ZRM}\)
3. \((4x)^{-3}.(4x)^{-8}=(4x)^{-3+(-8)}=(4x)^{-11}=(\frac{1}{4}\frac{1}{x})^{11}\left[=\frac{1}{4194304} \frac{1}{x^{11}}\right]=\text{ZRM}\)
4. \((\frac{16}{3}c)^{-3}:(\frac{16}{3}c)^{-5}=(\frac{16}{3}c)^{-3-(-5)}=(\frac{16}{3}c)^{2}\left[ =\frac{256}{9}c^{2} \right]\)
5. \((\frac{7}{4})^{2}.(2)^{2}=(\frac{7}{4}2)^{2}=(\frac{7}{2})^{2}=\left[\frac{49}{4}\right]\)
6. \((-\frac{9}{20})^{-2}=(-\frac{20}{9})^{2}=+\frac{20^{2}}{9^{2}}= \left[=\frac{400}{81}\right]\)
7. \((\frac{5}{8}c)^{4}.(\frac{5}{8}c)^{9}=(\frac{5}{8}c)^{4+9}=(\frac{5}{8}c)^{13}\left[=\frac{1220703125}{549755813888}c^{13}\right]=\text{ZRM}\)
8. \((-\frac{3}{10})^{-6}=(-\frac{10}{3})^{6}=+\frac{10^{6}}{3^{6}}=\text{ZRM}= \left[=\frac{1000000}{729}\right]\)
9. \((\frac{17}{5}a)^{-4}:(\frac{17}{5}a)^{5}=(\frac{17}{5}a)^{-4-5}=(\frac{17}{5}a)^{-9}=(\frac{5}{17}\frac{1}{a})^{9}=\text{ZRM}\left[ =\frac{1953125}{118587876497} \frac{1}{a^{9}} \right]\)
10. \((-\frac{13}{14})^{-6}=(-\frac{14}{13})^{6}=+\frac{14^{6}}{13^{6}}=\text{ZRM}= \left[=\frac{7529536}{4826809}\right]\)
11. \((\frac{18}{17}y)^{6}.(\frac{18}{17}y)^{-10}=(\frac{18}{17}y)^{6+(-10)}=(\frac{18}{17}y)^{-4}=(\frac{17}{18}\frac{1}{y})^{4}\left[=\frac{83521}{104976} \frac{1}{y^{4}}\right]=\text{ZRM}\)
12. \((-\frac{9}{20})^{-3}=(-\frac{20}{9})^{3}=-\frac{20^{3}}{9^{3}}=\text{ZRM}= \left[=-\frac{8000}{729}\right]\)