Rekenregels machten

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

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

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

Verbetersleutel

1. \((\frac{4}{17}x)^{-9}.(\frac{4}{17}x)^{-1}=(\frac{4}{17}x)^{-9+(-1)}=(\frac{4}{17}x)^{-10}=(\frac{17}{4}\frac{1}{x})^{10}\left[=\frac{2015993900449}{1048576} \frac{1}{x^{10}}\right]=\text{ZRM}\)
2. \(-(-\frac{2}{3})^{-5}=-(-\frac{3}{2})^{5}=+\frac{3^{5}}{2^{5}}=\text{ZRM}\left[=\frac{243}{32}\right]\)
3. \((\frac{17}{3})^{8}.(3)^{8}=(\frac{17}{3}3)^{8}=(17)^{8}=\text{ZRM}=\left[6975757441\right]\)
4. \((-5c^{10})^{-6}=(-5)^{-6}.(c^{10})^{-6}=(\frac{1}{-5})^{6}.(\frac{1}{c^{10}})^{6}=\text{ZRM}\left[=\frac{1}{15625} \frac{1}{c^{60}}\right]\)
5. \((5b^{5})^{-3}=(5)^{-3}.(b^{5})^{-3}=(\frac{1}{5})^{3}.(\frac{1}{b^{5}})^{3}=\text{ZRM}\left[=\frac{1}{125} \frac{1}{b^{15}}\right]\)
6. \((-\frac{5}{6})^{-3}=(-\frac{6}{5})^{3}=-\frac{6^{3}}{5^{3}}=\text{ZRM}= \left[=-\frac{216}{125}\right]\)
7. \((-4)^{-2}=(-\frac{1}{4})^{2}=+\frac{1^{2}}{4^{2}}= \left[=\frac{1}{16}\right]\)
8. \((\frac{7}{9}c)^{6}:(\frac{7}{9}c)^{-2}=(\frac{7}{9}c)^{6-(-2)}=(\frac{7}{9}c)^{8}=\text{ZRM}\left[ =\frac{5764801}{43046721}c^{8} \right]\)
9. \(-(-\frac{17}{5})^{-5}=-(-\frac{5}{17})^{5}=+\frac{5^{5}}{17^{5}}=\text{ZRM}\left[=\frac{3125}{1419857}\right]\)
10. \((19x)^{-6}.(19x)^{-10}=(19x)^{-6+(-10)}=(19x)^{-16}=(\frac{1}{19}\frac{1}{x})^{16}\left[=\frac{1}{2.8844141356762E+20} \frac{1}{x^{16}}\right]=\text{ZRM}\)
11. \((11y)^{2}.(11y)^{-5}=(11y)^{2+(-5)}=(11y)^{-3}=(\frac{1}{11}\frac{1}{y})^{3}\left[=\frac{1}{1331} \frac{1}{y^{3}}\right]=\text{ZRM}\)
12. \((16y^{3})^{6}=(16)^{6}.(y^{3})^{6}=\text{ZRM}\left[=16777216y^{18}\right]\)