Rekenregels machten

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

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

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

Verbetersleutel

1. \((\frac{5}{13}c)^{-2}.(\frac{5}{13}c)^{-4}=(\frac{5}{13}c)^{-2+(-4)}=(\frac{5}{13}c)^{-6}=(\frac{13}{5}\frac{1}{c})^{6}\left[=\frac{4826809}{15625} \frac{1}{c^{6}}\right]=\text{ZRM}\)
2. \((\frac{4}{5})^{-8}.(3)^{-8}=(\frac{4}{5}3)^{-8}=(\frac{12}{5})^{-8}=(\frac{5}{12})^{8}=\text{ZRM}=\left[\frac{390625}{429981696}\right]\)
3. \((\frac{3}{13}y)^{-7}.(\frac{3}{13}y)^{-1}=(\frac{3}{13}y)^{-7+(-1)}=(\frac{3}{13}y)^{-8}=(\frac{13}{3}\frac{1}{y})^{8}\left[=\frac{815730721}{6561} \frac{1}{y^{8}}\right]=\text{ZRM}\)
4. \(-(-\frac{3}{8})^{-4}=-(-\frac{8}{3})^{4}=-\frac{8^{4}}{3^{4}}=\text{ZRM}\left[=-\frac{4096}{81}\right]\)
5. \((\frac{17}{20}a)^{5}:(\frac{17}{20}a)^{7}=(\frac{17}{20}a)^{5-7}=(\frac{17}{20}a)^{-2}=(\frac{20}{17}\frac{1}{a})^{2}\left[ =\frac{400}{289} \frac{1}{a^{2}} \right]\)
6. \((\frac{2}{5}x)^{6}.(\frac{2}{5}x)^{2}=(\frac{2}{5}x)^{6+2}=(\frac{2}{5}x)^{8}\left[=\frac{256}{390625}x^{8}\right]=\text{ZRM}\)
7. \(-(-\frac{4}{3})^{-4}=-(-\frac{3}{4})^{4}=-\frac{3^{4}}{4^{4}}=\text{ZRM}\left[=-\frac{81}{256}\right]\)
8. \(-(-\frac{5}{7})^{-2}=-(-\frac{7}{5})^{2}=-\frac{7^{2}}{5^{2}}\left[=-\frac{49}{25}\right]\)
9. \((4x)^{-10}.(4x)^{8}=(4x)^{-10+8}=(4x)^{-2}=(\frac{1}{4}\frac{1}{x})^{2}\left[=\frac{1}{16} \frac{1}{x^{2}}\right]\)
10. \((\frac{4}{3})^{8}.(\frac{19}{6})^{8}=(\frac{4}{3}\frac{19}{6})^{8}=(\frac{38}{9})^{8}=\text{ZRM}=\left[\frac{4347792138496}{43046721}\right]\)
11. \(-(-\frac{15}{7})^{-3}=-(-\frac{7}{15})^{3}=+\frac{7^{3}}{15^{3}}=\text{ZRM}\left[=\frac{343}{3375}\right]\)
12. \((\frac{2}{7}c)^{-3}:(\frac{2}{7}c)^{-6}=(\frac{2}{7}c)^{-3-(-6)}=(\frac{2}{7}c)^{3}=\text{ZRM}\left[ =\frac{8}{343}c^{3} \right]\)