Rekenregels machten

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

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

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

Verbetersleutel

1. \((\frac{16}{19}a)^{-9}:(\frac{16}{19}a)^{-3}=(\frac{16}{19}a)^{-9-(-3)}=(\frac{16}{19}a)^{-6}=(\frac{19}{16}\frac{1}{a})^{6}=\text{ZRM}\left[ =\frac{47045881}{16777216} \frac{1}{a^{6}} \right]\)
2. \((\frac{4}{7}x)^{-6}:(\frac{4}{7}x)^{5}=(\frac{4}{7}x)^{-6-5}=(\frac{4}{7}x)^{-11}=(\frac{7}{4}\frac{1}{x})^{11}=\text{ZRM}\left[ =\frac{1977326743}{4194304} \frac{1}{x^{11}} \right]\)
3. \((\frac{13}{14}c)^{-5}.(\frac{13}{14}c)^{5}=(\frac{13}{14}c)^{-5+5}=(\frac{13}{14}c)^{0}\left[=1c^{0}\right]\left[=1\right]\)
4. \((\frac{20}{7}a)^{5}.(\frac{20}{7}a)^{3}=(\frac{20}{7}a)^{5+3}=(\frac{20}{7}a)^{8}\left[=\frac{25600000000}{5764801}a^{8}\right]=\text{ZRM}\)
5. \((\frac{3}{19}c)^{3}:(\frac{3}{19}c)^{8}=(\frac{3}{19}c)^{3-8}=(\frac{3}{19}c)^{-5}=(\frac{19}{3}\frac{1}{c})^{5}=\text{ZRM}\left[ =\frac{2476099}{243} \frac{1}{c^{5}} \right]\)
6. \((\frac{2}{3}y)^{9}.(\frac{2}{3}y)^{-1}=(\frac{2}{3}y)^{9+(-1)}=(\frac{2}{3}y)^{8}\left[=\frac{256}{6561}y^{8}\right]=\text{ZRM}\)
7. \(-(-\frac{11}{10})^{-2}=-(-\frac{10}{11})^{2}=-\frac{10^{2}}{11^{2}}\left[=-\frac{100}{121}\right]\)
8. \((-6c^{9})^{-6}=(-6)^{-6}.(c^{9})^{-6}=(\frac{1}{-6})^{6}.(\frac{1}{c^{9}})^{6}=\text{ZRM}\left[=\frac{1}{46656} \frac{1}{c^{54}}\right]\)
9. \((\frac{4}{9})^{-7}.(5)^{-7}=(\frac{4}{9}5)^{-7}=(\frac{20}{9})^{-7}=(\frac{9}{20})^{7}=\text{ZRM}=\left[\frac{4782969}{1280000000}\right]\)
10. \((\frac{9}{5})^{8}.(3)^{8}=(\frac{9}{5}3)^{8}=(\frac{27}{5})^{8}=\text{ZRM}=\left[\frac{282429536481}{390625}\right]\)
11. \(-(-\frac{3}{7})^{-6}=-(-\frac{7}{3})^{6}=-\frac{7^{6}}{3^{6}}=\text{ZRM}\left[=-\frac{117649}{729}\right]\)
12. \((19y^{5})^{-8}=(19)^{-8}.(y^{5})^{-8}=(\frac{1}{19})^{8}.(\frac{1}{y^{5}})^{8}=\text{ZRM}\left[=\frac{1}{16983563041} \frac{1}{y^{40}}\right]\)