Rekenregels machten

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

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

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

Verbetersleutel

1. \((\frac{14}{17}x)^{-1}.(\frac{14}{17}x)^{-9}=(\frac{14}{17}x)^{-1+(-9)}=(\frac{14}{17}x)^{-10}=(\frac{17}{14}\frac{1}{x})^{10}\left[=\frac{2015993900449}{289254654976} \frac{1}{x^{10}}\right]=\text{ZRM}\)
2. \((-9)^{-6}=(-\frac{1}{9})^{6}=+\frac{1^{6}}{9^{6}}=\text{ZRM}= \left[=\frac{1}{531441}\right]\)
3. \((\frac{13}{14})^{10}.(\frac{17}{14})^{10}=(\frac{13}{14}\frac{17}{14})^{10}=(\frac{221}{196})^{10}=\text{ZRM}=\left[\frac{2.7792187869268E+23}{8.3668255425285E+22}\right]\)
4. \((\frac{3}{10}a)^{-7}.(\frac{3}{10}a)^{1}=(\frac{3}{10}a)^{-7+1}=(\frac{3}{10}a)^{-6}=(\frac{10}{3}\frac{1}{a})^{6}\left[=\frac{1000000}{729} \frac{1}{a^{6}}\right]=\text{ZRM}\)
5. \((17a^{5})^{-5}=(17)^{-5}.(a^{5})^{-5}=(\frac{1}{17})^{5}.(\frac{1}{a^{5}})^{5}=\text{ZRM}\left[=\frac{1}{1419857} \frac{1}{a^{25}}\right]\)
6. \(-(-\frac{2}{5})^{-5}=-(-\frac{5}{2})^{5}=+\frac{5^{5}}{2^{5}}=\text{ZRM}\left[=\frac{3125}{32}\right]\)
7. \((-2c^{8})^{6}=(-2)^{6}.(c^{8})^{6}=\text{ZRM}\left[=64c^{48}\right]\)
8. \((6x^{4})^{4}=(6)^{4}.(x^{4})^{4}=\text{ZRM}\left[=1296x^{16}\right]\)
9. \(-(-\frac{17}{12})^{-2}=-(-\frac{12}{17})^{2}=-\frac{12^{2}}{17^{2}}\left[=-\frac{144}{289}\right]\)
10. \((\frac{17}{7}x)^{1}:(\frac{17}{7}x)^{1}=(\frac{17}{7}x)^{1-1}=(\frac{17}{7}x)^{0}=1x^{0}\left[= 1 \right]\)
11. \(-(-\frac{3}{5})^{-6}=-(-\frac{5}{3})^{6}=-\frac{5^{6}}{3^{6}}=\text{ZRM}\left[=-\frac{15625}{729}\right]\)
12. \((\frac{20}{17}b)^{10}:(\frac{20}{17}b)^{1}=(\frac{20}{17}b)^{10-1}=(\frac{20}{17}b)^{9}=\text{ZRM}\left[ =\frac{512000000000}{118587876497}b^{9} \right]\)