Rekenregels machten

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

1. \((-17x^{6})^{-6}\)
2. \((\frac{7}{13}x)^{-4}:(\frac{7}{13}x)^{-4}\)
3. \((\frac{11}{17}y)^{-10}:(\frac{11}{17}y)^{-9}\)
4. \((\frac{12}{7}y)^{-10}:(\frac{12}{7}y)^{-1}\)
5. \((-\frac{5}{4})^{-6}\)
6. \((\frac{12}{13}y)^{8}:(\frac{12}{13}y)^{-10}\)
7. \((-9c^{4})^{-5}\)
8. \((\frac{6}{5})^{4}.(\frac{5}{3})^{4}\)
9. \((15c^{9})^{-7}\)
10. \((\frac{14}{11}b)^{-8}:(\frac{14}{11}b)^{6}\)
11. \((-\frac{5}{17})^{-6}\)
12. \((-\frac{5}{8})^{-6}\)

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

Verbetersleutel

1. \((-17x^{6})^{-6}=(-17)^{-6}.(x^{6})^{-6}=(\frac{1}{-17})^{6}.(\frac{1}{x^{6}})^{6}=\text{ZRM}\left[=\frac{1}{24137569} \frac{1}{x^{36}}\right]\)
2. \((\frac{7}{13}x)^{-4}:(\frac{7}{13}x)^{-4}=(\frac{7}{13}x)^{-4-(-4)}=(\frac{7}{13}x)^{0}=1x^{0}\left[= 1 \right]\)
3. \((\frac{11}{17}y)^{-10}:(\frac{11}{17}y)^{-9}=(\frac{11}{17}y)^{-10-(-9)}=(\frac{11}{17}y)^{-1}=(\frac{17}{11}\frac{1}{y})^{1}\left[ =\frac{17}{11} \frac{1}{y^{1}} \right]\)
4. \((\frac{12}{7}y)^{-10}:(\frac{12}{7}y)^{-1}=(\frac{12}{7}y)^{-10-(-1)}=(\frac{12}{7}y)^{-9}=(\frac{7}{12}\frac{1}{y})^{9}=\text{ZRM}\left[ =\frac{40353607}{5159780352} \frac{1}{y^{9}} \right]\)
5. \((-\frac{5}{4})^{-6}=(-\frac{4}{5})^{6}=+\frac{4^{6}}{5^{6}}=\text{ZRM}= \left[=\frac{4096}{15625}\right]\)
6. \((\frac{12}{13}y)^{8}:(\frac{12}{13}y)^{-10}=(\frac{12}{13}y)^{8-(-10)}=(\frac{12}{13}y)^{18}=\text{ZRM}\left[ =\frac{2.6623333280885E+19}{1.1245540695196E+20}y^{18} \right]\)
7. \((-9c^{4})^{-5}=(-9)^{-5}.(c^{4})^{-5}=(\frac{1}{-9})^{5}.(\frac{1}{c^{4}})^{5}=\text{ZRM}\left[=(\frac{1}{-59049}) \frac{1}{c^{20}}\right]\)
8. \((\frac{6}{5})^{4}.(\frac{5}{3})^{4}=(\frac{6}{5}\frac{5}{3})^{4}=(2)^{4}=\text{ZRM}=\left[16\right]\)
9. \((15c^{9})^{-7}=(15)^{-7}.(c^{9})^{-7}=(\frac{1}{15})^{7}.(\frac{1}{c^{9}})^{7}=\text{ZRM}\left[=\frac{1}{170859375} \frac{1}{c^{63}}\right]\)
10. \((\frac{14}{11}b)^{-8}:(\frac{14}{11}b)^{6}=(\frac{14}{11}b)^{-8-6}=(\frac{14}{11}b)^{-14}=(\frac{11}{14}\frac{1}{b})^{14}=\text{ZRM}\left[ =\frac{379749833583241}{11112006825558016} \frac{1}{b^{14}} \right]\)
11. \((-\frac{5}{17})^{-6}=(-\frac{17}{5})^{6}=+\frac{17^{6}}{5^{6}}=\text{ZRM}= \left[=\frac{24137569}{15625}\right]\)
12. \((-\frac{5}{8})^{-6}=(-\frac{8}{5})^{6}=+\frac{8^{6}}{5^{6}}=\text{ZRM}= \left[=\frac{262144}{15625}\right]\)