Rekenregels machten

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

1. \((\frac{17}{16})^{-8}.(\frac{3}{20})^{-8}\)
2. \((\frac{6}{5}a)^{10}:(\frac{6}{5}a)^{-9}\)
3. \((\frac{6}{7}x)^{-5}:(\frac{6}{7}x)^{-5}\)
4. \(-(-\frac{7}{5})^{-1}\)
5. \(-(-\frac{7}{10})^{-5}\)
6. \((-1x^{5})^{-6}\)
7. \((\frac{11}{18})^{2}.(\frac{11}{19})^{2}\)
8. \((3c)^{-9}:(3c)^{1}\)
9. \((-\frac{17}{4})^{-1}\)
10. \((-\frac{14}{13})^{-4}\)
11. \((-\frac{5}{7})^{-5}\)
12. \((3x)^{-8}:(3x)^{7}\)

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

Verbetersleutel

1. \((\frac{17}{16})^{-8}.(\frac{3}{20})^{-8}=(\frac{17}{16}\frac{3}{20})^{-8}=(\frac{51}{320})^{-8}=(\frac{320}{51})^{8}=\text{ZRM}=\left[\frac{1.099511627776E+20}{45767944570401}\right]\)
2. \((\frac{6}{5}a)^{10}:(\frac{6}{5}a)^{-9}=(\frac{6}{5}a)^{10-(-9)}=(\frac{6}{5}a)^{19}=\text{ZRM}\left[ =\frac{609359740010496}{19073486328125}a^{19} \right]\)
3. \((\frac{6}{7}x)^{-5}:(\frac{6}{7}x)^{-5}=(\frac{6}{7}x)^{-5-(-5)}=(\frac{6}{7}x)^{0}=1x^{0}\left[= 1 \right]\)
4. \(-(-\frac{7}{5})^{-1}=-(-\frac{5}{7})^{1}=+\frac{5^{1}}{7^{1}}\left[=\frac{5}{7}\right]\)
5. \(-(-\frac{7}{10})^{-5}=-(-\frac{10}{7})^{5}=+\frac{10^{5}}{7^{5}}=\text{ZRM}\left[=\frac{100000}{16807}\right]\)
6. \((-1x^{5})^{-6}=(-1)^{-6}.(x^{5})^{-6}=(\frac{1}{-1})^{6}.(\frac{1}{x^{5}})^{6}=\text{ZRM}\left[=1 \frac{1}{x^{30}}\right]\)
7. \((\frac{11}{18})^{2}.(\frac{11}{19})^{2}=(\frac{11}{18}\frac{11}{19})^{2}=(\frac{121}{342})^{2}=\left[\frac{14641}{116964}\right]\)
8. \((3c)^{-9}:(3c)^{1}=(3c)^{-9-1}=(3c)^{-10}=(\frac{1}{3}\frac{1}{c})^{10}=\text{ZRM}\left[ =\frac{1}{59049} \frac{1}{c^{10}} \right]\)
9. \((-\frac{17}{4})^{-1}=(-\frac{4}{17})^{1}=-\frac{4^{1}}{17^{1}}= \left[=-\frac{4}{17}\right]\)
10. \((-\frac{14}{13})^{-4}=(-\frac{13}{14})^{4}=+\frac{13^{4}}{14^{4}}=\text{ZRM}= \left[=\frac{28561}{38416}\right]\)
11. \((-\frac{5}{7})^{-5}=(-\frac{7}{5})^{5}=-\frac{7^{5}}{5^{5}}=\text{ZRM}= \left[=-\frac{16807}{3125}\right]\)
12. \((3x)^{-8}:(3x)^{7}=(3x)^{-8-7}=(3x)^{-15}=(\frac{1}{3}\frac{1}{x})^{15}=\text{ZRM}\left[ =\frac{1}{14348907} \frac{1}{x^{15}} \right]\)