Rekenregels machten

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

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

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

Verbetersleutel

1. \((-10y^{10})^{8}=(-10)^{8}.(y^{10})^{8}=\text{ZRM}\left[=100000000y^{80}\right]\)
2. \((\frac{3}{5})^{-9}.(\frac{3}{4})^{-9}=(\frac{3}{5}\frac{3}{4})^{-9}=(\frac{9}{20})^{-9}=(\frac{20}{9})^{9}=\text{ZRM}=\left[\frac{512000000000}{387420489}\right]\)
3. \((-\frac{13}{14})^{-2}=(-\frac{14}{13})^{2}=+\frac{14^{2}}{13^{2}}= \left[=\frac{196}{169}\right]\)
4. \((-20b^{6})^{8}=(-20)^{8}.(b^{6})^{8}=\text{ZRM}\left[=25600000000b^{48}\right]\)
5. \((\frac{5}{19}b)^{-2}.(\frac{5}{19}b)^{10}=(\frac{5}{19}b)^{-2+10}=(\frac{5}{19}b)^{8}\left[=\frac{390625}{16983563041}b^{8}\right]=\text{ZRM}\)
6. \((4c)^{6}.(4c)^{1}=(4c)^{6+1}=(4c)^{7}\left[=16384c^{7}\right]=\text{ZRM}\)
7. \((18y^{6})^{-8}=(18)^{-8}.(y^{6})^{-8}=(\frac{1}{18})^{8}.(\frac{1}{y^{6}})^{8}=\text{ZRM}\left[=\frac{1}{11019960576} \frac{1}{y^{48}}\right]\)
8. \(-(-\frac{4}{19})^{-3}=-(-\frac{19}{4})^{3}=+\frac{19^{3}}{4^{3}}=\text{ZRM}\left[=\frac{6859}{64}\right]\)
9. \((-\frac{9}{17})^{-1}=(-\frac{17}{9})^{1}=-\frac{17^{1}}{9^{1}}= \left[=-\frac{17}{9}\right]\)
10. \((\frac{16}{9}y)^{3}:(\frac{16}{9}y)^{5}=(\frac{16}{9}y)^{3-5}=(\frac{16}{9}y)^{-2}=(\frac{9}{16}\frac{1}{y})^{2}\left[ =\frac{81}{256} \frac{1}{y^{2}} \right]\)
11. \((-2a^{6})^{-7}=(-2)^{-7}.(a^{6})^{-7}=(\frac{1}{-2})^{7}.(\frac{1}{a^{6}})^{7}=\text{ZRM}\left[=(\frac{1}{-128}) \frac{1}{a^{42}}\right]\)
12. \((\frac{2}{5}y)^{1}:(\frac{2}{5}y)^{-10}=(\frac{2}{5}y)^{1-(-10)}=(\frac{2}{5}y)^{11}=\text{ZRM}\left[ =\frac{2048}{48828125}y^{11} \right]\)