Rekenregels machten

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

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

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

Verbetersleutel

1. \((\frac{20}{9})^{-2}.(\frac{5}{2})^{-2}=(\frac{20}{9}\frac{5}{2})^{-2}=(\frac{50}{9})^{-2}=(\frac{9}{50})^{2}=\left[\frac{81}{2500}\right]\)
2. \((\frac{10}{7}y)^{-4}.(\frac{10}{7}y)^{-3}=(\frac{10}{7}y)^{-4+(-3)}=(\frac{10}{7}y)^{-7}=(\frac{7}{10}\frac{1}{y})^{7}\left[=\frac{823543}{10000000} \frac{1}{y^{7}}\right]=\text{ZRM}\)
3. \((-\frac{6}{19})^{-6}=(-\frac{19}{6})^{6}=+\frac{19^{6}}{6^{6}}=\text{ZRM}= \left[=\frac{47045881}{46656}\right]\)
4. \((-2)^{-6}=(-\frac{1}{2})^{6}=+\frac{1^{6}}{2^{6}}=\text{ZRM}= \left[=\frac{1}{64}\right]\)
5. \(-(-\frac{8}{5})^{-4}=-(-\frac{5}{8})^{4}=-\frac{5^{4}}{8^{4}}=\text{ZRM}\left[=-\frac{625}{4096}\right]\)
6. \(-(-\frac{9}{2})^{-4}=-(-\frac{2}{9})^{4}=-\frac{2^{4}}{9^{4}}=\text{ZRM}\left[=-\frac{16}{6561}\right]\)
7. \((-17x^{5})^{6}=(-17)^{6}.(x^{5})^{6}=\text{ZRM}\left[=24137569x^{30}\right]\)
8. \(-(-\frac{12}{7})^{-1}=-(-\frac{7}{12})^{1}=+\frac{7^{1}}{12^{1}}\left[=\frac{7}{12}\right]\)
9. \((\frac{9}{19}x)^{3}.(\frac{9}{19}x)^{-7}=(\frac{9}{19}x)^{3+(-7)}=(\frac{9}{19}x)^{-4}=(\frac{19}{9}\frac{1}{x})^{4}\left[=\frac{130321}{6561} \frac{1}{x^{4}}\right]=\text{ZRM}\)
10. \((\frac{19}{15}x)^{-10}.(\frac{19}{15}x)^{1}=(\frac{19}{15}x)^{-10+1}=(\frac{19}{15}x)^{-9}=(\frac{15}{19}\frac{1}{x})^{9}\left[=\frac{38443359375}{322687697779} \frac{1}{x^{9}}\right]=\text{ZRM}\)
11. \((\frac{16}{17}b)^{7}.(\frac{16}{17}b)^{4}=(\frac{16}{17}b)^{7+4}=(\frac{16}{17}b)^{11}\left[=\frac{17592186044416}{34271896307633}b^{11}\right]=\text{ZRM}\)
12. \(-(-19)^{-6}=-(-\frac{1}{19})^{6}=-\frac{1^{6}}{19^{6}}=\text{ZRM}\left[=-\frac{1}{47045881}\right]\)