Rekenregels machten

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

1. \((\frac{2}{3}c)^{1}.(\frac{2}{3}c)^{-8}\)
2. \((3x^{8})^{6}\)
3. \((-\frac{4}{3})^{-3}\)
4. \((-\frac{6}{5})^{-6}\)
5. \((\frac{13}{7})^{7}.(\frac{13}{9})^{7}\)
6. \((-5)^{-6}\)
7. \(-(-\frac{4}{3})^{-2}\)
8. \(-(-\frac{17}{4})^{-5}\)
9. \((17y)^{2}.(17y)^{-2}\)
10. \((-15a^{9})^{-4}\)
11. \((-9y^{5})^{-8}\)
12. \((\frac{14}{15})^{-5}.(\frac{13}{2})^{-5}\)

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

Verbetersleutel

1. \((\frac{2}{3}c)^{1}.(\frac{2}{3}c)^{-8}=(\frac{2}{3}c)^{1+(-8)}=(\frac{2}{3}c)^{-7}=(\frac{3}{2}\frac{1}{c})^{7}\left[=\frac{2187}{128} \frac{1}{c^{7}}\right]=\text{ZRM}\)
2. \((3x^{8})^{6}=(3)^{6}.(x^{8})^{6}=\text{ZRM}\left[=729x^{48}\right]\)
3. \((-\frac{4}{3})^{-3}=(-\frac{3}{4})^{3}=-\frac{3^{3}}{4^{3}}=\text{ZRM}= \left[=-\frac{27}{64}\right]\)
4. \((-\frac{6}{5})^{-6}=(-\frac{5}{6})^{6}=+\frac{5^{6}}{6^{6}}=\text{ZRM}= \left[=\frac{15625}{46656}\right]\)
5. \((\frac{13}{7})^{7}.(\frac{13}{9})^{7}=(\frac{13}{7}\frac{13}{9})^{7}=(\frac{169}{63})^{7}=\text{ZRM}=\left[\frac{3937376385699289}{3938980639167}\right]\)
6. \((-5)^{-6}=(-\frac{1}{5})^{6}=+\frac{1^{6}}{5^{6}}=\text{ZRM}= \left[=\frac{1}{15625}\right]\)
7. \(-(-\frac{4}{3})^{-2}=-(-\frac{3}{4})^{2}=-\frac{3^{2}}{4^{2}}\left[=-\frac{9}{16}\right]\)
8. \(-(-\frac{17}{4})^{-5}=-(-\frac{4}{17})^{5}=+\frac{4^{5}}{17^{5}}=\text{ZRM}\left[=\frac{1024}{1419857}\right]\)
9. \((17y)^{2}.(17y)^{-2}=(17y)^{2+(-2)}=(17y)^{0}\left[=1y^{0}\right]\left[=1\right]\)
10. \((-15a^{9})^{-4}=(-15)^{-4}.(a^{9})^{-4}=(\frac{1}{-15})^{4}.(\frac{1}{a^{9}})^{4}=\text{ZRM}\left[=\frac{1}{50625} \frac{1}{a^{36}}\right]\)
11. \((-9y^{5})^{-8}=(-9)^{-8}.(y^{5})^{-8}=(\frac{1}{-9})^{8}.(\frac{1}{y^{5}})^{8}=\text{ZRM}\left[=\frac{1}{43046721} \frac{1}{y^{40}}\right]\)
12. \((\frac{14}{15})^{-5}.(\frac{13}{2})^{-5}=(\frac{14}{15}\frac{13}{2})^{-5}=(\frac{91}{15})^{-5}=(\frac{15}{91})^{5}=\text{ZRM}=\left[\frac{759375}{6240321451}\right]\)