Rekenregels machten

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

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

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

Verbetersleutel

1. \(-(-\frac{5}{2})^{-2}=-(-\frac{2}{5})^{2}=-\frac{2^{2}}{5^{2}}\left[=-\frac{4}{25}\right]\)
2. \((-12c^{2})^{5}=(-12)^{5}.(c^{2})^{5}=\text{ZRM}\left[=(-248832)c^{10}\right]\)
3. \((\frac{14}{17}c)^{10}:(\frac{14}{17}c)^{4}=(\frac{14}{17}c)^{10-4}=(\frac{14}{17}c)^{6}=\text{ZRM}\left[ =\frac{7529536}{24137569}c^{6} \right]\)
4. \((-\frac{5}{4})^{-5}=(-\frac{4}{5})^{5}=-\frac{4^{5}}{5^{5}}=\text{ZRM}= \left[=-\frac{1024}{3125}\right]\)
5. \((\frac{17}{12})^{9}.(\frac{11}{8})^{9}=(\frac{17}{12}\frac{11}{8})^{9}=(\frac{187}{96})^{9}=\text{ZRM}=\left[\frac{2.7962400956669E+20}{692533995824480256}\right]\)
6. \((-\frac{11}{5})^{-3}=(-\frac{5}{11})^{3}=-\frac{5^{3}}{11^{3}}=\text{ZRM}= \left[=-\frac{125}{1331}\right]\)
7. \((\frac{6}{7}b)^{1}:(\frac{6}{7}b)^{-3}=(\frac{6}{7}b)^{1-(-3)}=(\frac{6}{7}b)^{4}=\text{ZRM}\left[ =\frac{1296}{2401}b^{4} \right]\)
8. \((\frac{4}{7})^{1}.(\frac{19}{4})^{1}=(\frac{4}{7}\frac{19}{4})^{1}=(\frac{19}{7})^{1}=\left[\frac{19}{7}\right]\)
9. \((-5)^{-2}=(-\frac{1}{5})^{2}=+\frac{1^{2}}{5^{2}}= \left[=\frac{1}{25}\right]\)
10. \(-(-16)^{-4}=-(-\frac{1}{16})^{4}=-\frac{1^{4}}{16^{4}}=\text{ZRM}\left[=-\frac{1}{65536}\right]\)
11. \((12c)^{-5}.(12c)^{-2}=(12c)^{-5+(-2)}=(12c)^{-7}=(\frac{1}{12}\frac{1}{c})^{7}\left[=\frac{1}{35831808} \frac{1}{c^{7}}\right]=\text{ZRM}\)
12. \((\frac{4}{17}y)^{-1}:(\frac{4}{17}y)^{10}=(\frac{4}{17}y)^{-1-10}=(\frac{4}{17}y)^{-11}=(\frac{17}{4}\frac{1}{y})^{11}=\text{ZRM}\left[ =\frac{34271896307633}{4194304} \frac{1}{y^{11}} \right]\)