Rekenregels machten

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

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

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

Verbetersleutel

1. \((\frac{19}{2})^{-6}.(\frac{5}{4})^{-6}=(\frac{19}{2}\frac{5}{4})^{-6}=(\frac{95}{8})^{-6}=(\frac{8}{95})^{6}=\text{ZRM}=\left[\frac{262144}{735091890625}\right]\)
2. \((9x^{6})^{2}=(9)^{2}.(x^{6})^{2}=\text{ZRM}\left[=81x^{12}\right]\)
3. \((\frac{7}{10})^{10}.(6)^{10}=(\frac{7}{10}6)^{10}=(\frac{21}{5})^{10}=\text{ZRM}=\left[\frac{16679880978201}{9765625}\right]\)
4. \((\frac{3}{2}a)^{-9}.(\frac{3}{2}a)^{7}=(\frac{3}{2}a)^{-9+7}=(\frac{3}{2}a)^{-2}=(\frac{2}{3}\frac{1}{a})^{2}\left[=\frac{4}{9} \frac{1}{a^{2}}\right]\)
5. \(-(-\frac{7}{19})^{-3}=-(-\frac{19}{7})^{3}=+\frac{19^{3}}{7^{3}}=\text{ZRM}\left[=\frac{6859}{343}\right]\)
6. \((13b^{4})^{8}=(13)^{8}.(b^{4})^{8}=\text{ZRM}\left[=815730721b^{32}\right]\)
7. \(-(-\frac{11}{13})^{-4}=-(-\frac{13}{11})^{4}=-\frac{13^{4}}{11^{4}}=\text{ZRM}\left[=-\frac{28561}{14641}\right]\)
8. \((\frac{16}{17})^{-4}.(3)^{-4}=(\frac{16}{17}3)^{-4}=(\frac{48}{17})^{-4}=(\frac{17}{48})^{4}=\text{ZRM}=\left[\frac{83521}{5308416}\right]\)
9. \((\frac{13}{2}y)^{-6}.(\frac{13}{2}y)^{1}=(\frac{13}{2}y)^{-6+1}=(\frac{13}{2}y)^{-5}=(\frac{2}{13}\frac{1}{y})^{5}\left[=\frac{32}{371293} \frac{1}{y^{5}}\right]=\text{ZRM}\)
10. \((\frac{5}{8}c)^{-8}.(\frac{5}{8}c)^{-5}=(\frac{5}{8}c)^{-8+(-5)}=(\frac{5}{8}c)^{-13}=(\frac{8}{5}\frac{1}{c})^{13}\left[=\frac{549755813888}{1220703125} \frac{1}{c^{13}}\right]=\text{ZRM}\)
11. \(-(-5)^{-5}=-(-\frac{1}{5})^{5}=+\frac{1^{5}}{5^{5}}=\text{ZRM}\left[=\frac{1}{3125}\right]\)
12. \((\frac{8}{15}y)^{-1}.(\frac{8}{15}y)^{-4}=(\frac{8}{15}y)^{-1+(-4)}=(\frac{8}{15}y)^{-5}=(\frac{15}{8}\frac{1}{y})^{5}\left[=\frac{759375}{32768} \frac{1}{y^{5}}\right]=\text{ZRM}\)