Rekenregels machten

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

1. \((\frac{7}{17}a)^{1}.(\frac{7}{17}a)^{-10}\)
2. \((-14x^{5})^{-5}\)
3. \((-4a^{8})^{2}\)
4. \((\frac{8}{15}b)^{-8}.(\frac{8}{15}b)^{-7}\)
5. \(-(-\frac{16}{17})^{-2}\)
6. \((\frac{3}{16})^{-2}.(\frac{8}{13})^{-2}\)
7. \((15c)^{-1}:(15c)^{-4}\)
8. \((-\frac{20}{19})^{-6}\)
9. \(-(-\frac{17}{19})^{-3}\)
10. \((-\frac{12}{7})^{-2}\)
11. \((\frac{7}{3}y)^{4}:(\frac{7}{3}y)^{7}\)
12. \((\frac{3}{2}b)^{-2}.(\frac{3}{2}b)^{-2}\)

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

Verbetersleutel

1. \((\frac{7}{17}a)^{1}.(\frac{7}{17}a)^{-10}=(\frac{7}{17}a)^{1+(-10)}=(\frac{7}{17}a)^{-9}=(\frac{17}{7}\frac{1}{a})^{9}\left[=\frac{118587876497}{40353607} \frac{1}{a^{9}}\right]=\text{ZRM}\)
2. \((-14x^{5})^{-5}=(-14)^{-5}.(x^{5})^{-5}=(\frac{1}{-14})^{5}.(\frac{1}{x^{5}})^{5}=\text{ZRM}\left[=(\frac{1}{-537824}) \frac{1}{x^{25}}\right]\)
3. \((-4a^{8})^{2}=(-4)^{2}.(a^{8})^{2}=\text{ZRM}\left[=16a^{16}\right]\)
4. \((\frac{8}{15}b)^{-8}.(\frac{8}{15}b)^{-7}=(\frac{8}{15}b)^{-8+(-7)}=(\frac{8}{15}b)^{-15}=(\frac{15}{8}\frac{1}{b})^{15}\left[=\frac{437893890380859375}{35184372088832} \frac{1}{b^{15}}\right]=\text{ZRM}\)
5. \(-(-\frac{16}{17})^{-2}=-(-\frac{17}{16})^{2}=-\frac{17^{2}}{16^{2}}\left[=-\frac{289}{256}\right]\)
6. \((\frac{3}{16})^{-2}.(\frac{8}{13})^{-2}=(\frac{3}{16}\frac{8}{13})^{-2}=(\frac{3}{26})^{-2}=(\frac{26}{3})^{2}=\left[\frac{676}{9}\right]\)
7. \((15c)^{-1}:(15c)^{-4}=(15c)^{-1-(-4)}=(15c)^{3}=\text{ZRM}\left[ =3375c^{3} \right]\)
8. \((-\frac{20}{19})^{-6}=(-\frac{19}{20})^{6}=+\frac{19^{6}}{20^{6}}=\text{ZRM}= \left[=\frac{47045881}{64000000}\right]\)
9. \(-(-\frac{17}{19})^{-3}=-(-\frac{19}{17})^{3}=+\frac{19^{3}}{17^{3}}=\text{ZRM}\left[=\frac{6859}{4913}\right]\)
10. \((-\frac{12}{7})^{-2}=(-\frac{7}{12})^{2}=+\frac{7^{2}}{12^{2}}= \left[=\frac{49}{144}\right]\)
11. \((\frac{7}{3}y)^{4}:(\frac{7}{3}y)^{7}=(\frac{7}{3}y)^{4-7}=(\frac{7}{3}y)^{-3}=(\frac{3}{7}\frac{1}{y})^{3}=\text{ZRM}\left[ =\frac{27}{343} \frac{1}{y^{3}} \right]\)
12. \((\frac{3}{2}b)^{-2}.(\frac{3}{2}b)^{-2}=(\frac{3}{2}b)^{-2+(-2)}=(\frac{3}{2}b)^{-4}=(\frac{2}{3}\frac{1}{b})^{4}\left[=\frac{16}{81} \frac{1}{b^{4}}\right]=\text{ZRM}\)