Rekenregels machten

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

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

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

Verbetersleutel

1. \((\frac{2}{3})^{-8}.(\frac{9}{8})^{-8}=(\frac{2}{3}\frac{9}{8})^{-8}=(\frac{3}{4})^{-8}=(\frac{4}{3})^{8}=\text{ZRM}=\left[\frac{65536}{6561}\right]\)
2. \((\frac{4}{3}a)^{8}.(\frac{4}{3}a)^{-10}=(\frac{4}{3}a)^{8+(-10)}=(\frac{4}{3}a)^{-2}=(\frac{3}{4}\frac{1}{a})^{2}\left[=\frac{9}{16} \frac{1}{a^{2}}\right]\)
3. \((20y^{5})^{8}=(20)^{8}.(y^{5})^{8}=\text{ZRM}\left[=25600000000y^{40}\right]\)
4. \((-\frac{12}{13})^{-4}=(-\frac{13}{12})^{4}=+\frac{13^{4}}{12^{4}}=\text{ZRM}= \left[=\frac{28561}{20736}\right]\)
5. \((-\frac{15}{19})^{-4}=(-\frac{19}{15})^{4}=+\frac{19^{4}}{15^{4}}=\text{ZRM}= \left[=\frac{130321}{50625}\right]\)
6. \((\frac{13}{17})^{3}.(4)^{3}=(\frac{13}{17}4)^{3}=(\frac{52}{17})^{3}=\text{ZRM}=\left[\frac{140608}{4913}\right]\)
7. \((\frac{4}{15}x)^{6}:(\frac{4}{15}x)^{-2}=(\frac{4}{15}x)^{6-(-2)}=(\frac{4}{15}x)^{8}=\text{ZRM}\left[ =\frac{65536}{2562890625}x^{8} \right]\)
8. \((\frac{15}{16})^{-2}.(\frac{19}{15})^{-2}=(\frac{15}{16}\frac{19}{15})^{-2}=(\frac{19}{16})^{-2}=(\frac{16}{19})^{2}=\left[\frac{256}{361}\right]\)
9. \((\frac{11}{10})^{-10}.(3)^{-10}=(\frac{11}{10}3)^{-10}=(\frac{33}{10})^{-10}=(\frac{10}{33})^{10}=\text{ZRM}=\left[\frac{10000000000}{1531578985264449}\right]\)
10. \((\frac{7}{9}y)^{9}.(\frac{7}{9}y)^{8}=(\frac{7}{9}y)^{9+8}=(\frac{7}{9}y)^{17}\left[=\frac{232630513987207}{16677181699666569}y^{17}\right]=\text{ZRM}\)
11. \((3)^{-6}.(2)^{-6}=(32)^{-6}=(6)^{-6}=(\frac{1}{6})^{6}=\text{ZRM}=\left[\frac{1}{46656}\right]\)
12. \((\frac{2}{5})^{5}.(\frac{13}{6})^{5}=(\frac{2}{5}\frac{13}{6})^{5}=(\frac{13}{15})^{5}=\text{ZRM}=\left[\frac{371293}{759375}\right]\)