Rekenregels machten

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

1. \(-(-\frac{17}{9})^{-3}\)
2. \(-(-\frac{2}{13})^{-6}\)
3. \((\frac{19}{9})^{-1}.(\frac{9}{16})^{-1}\)
4. \((\frac{12}{5})^{-7}.(\frac{18}{19})^{-7}\)
5. \(-(-\frac{12}{17})^{-2}\)
6. \((\frac{13}{18}b)^{-7}:(\frac{13}{18}b)^{7}\)
7. \((\frac{17}{9}y)^{-8}:(\frac{17}{9}y)^{7}\)
8. \((-2)^{-1}\)
9. \((\frac{11}{10})^{1}.(\frac{9}{10})^{1}\)
10. \(-(-3)^{-6}\)
11. \((\frac{2}{7}c)^{-6}.(\frac{2}{7}c)^{-9}\)
12. \((\frac{3}{4}y)^{-9}.(\frac{3}{4}y)^{2}\)

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

Verbetersleutel

1. \(-(-\frac{17}{9})^{-3}=-(-\frac{9}{17})^{3}=+\frac{9^{3}}{17^{3}}=\text{ZRM}\left[=\frac{729}{4913}\right]\)
2. \(-(-\frac{2}{13})^{-6}=-(-\frac{13}{2})^{6}=-\frac{13^{6}}{2^{6}}=\text{ZRM}\left[=-\frac{4826809}{64}\right]\)
3. \((\frac{19}{9})^{-1}.(\frac{9}{16})^{-1}=(\frac{19}{9}\frac{9}{16})^{-1}=(\frac{19}{16})^{-1}=(\frac{16}{19})^{1}=\left[\frac{16}{19}\right]\)
4. \((\frac{12}{5})^{-7}.(\frac{18}{19})^{-7}=(\frac{12}{5}\frac{18}{19})^{-7}=(\frac{216}{95})^{-7}=(\frac{95}{216})^{7}=\text{ZRM}=\left[\frac{69833729609375}{21936950640377856}\right]\)
5. \(-(-\frac{12}{17})^{-2}=-(-\frac{17}{12})^{2}=-\frac{17^{2}}{12^{2}}\left[=-\frac{289}{144}\right]\)
6. \((\frac{13}{18}b)^{-7}:(\frac{13}{18}b)^{7}=(\frac{13}{18}b)^{-7-7}=(\frac{13}{18}b)^{-14}=(\frac{18}{13}\frac{1}{b})^{14}=\text{ZRM}\left[ =\frac{374813367582081024}{3937376385699289} \frac{1}{b^{14}} \right]\)
7. \((\frac{17}{9}y)^{-8}:(\frac{17}{9}y)^{7}=(\frac{17}{9}y)^{-8-7}=(\frac{17}{9}y)^{-15}=(\frac{9}{17}\frac{1}{y})^{15}=\text{ZRM}\left[ =\frac{205891132094649}{2862423051509815793} \frac{1}{y^{15}} \right]\)
8. \((-2)^{-1}=(-\frac{1}{2})^{1}=-\frac{1^{1}}{2^{1}}= \left[=-\frac{1}{2}\right]\)
9. \((\frac{11}{10})^{1}.(\frac{9}{10})^{1}=(\frac{11}{10}\frac{9}{10})^{1}=(\frac{99}{100})^{1}=\left[\frac{99}{100}\right]\)
10. \(-(-3)^{-6}=-(-\frac{1}{3})^{6}=-\frac{1^{6}}{3^{6}}=\text{ZRM}\left[=-\frac{1}{729}\right]\)
11. \((\frac{2}{7}c)^{-6}.(\frac{2}{7}c)^{-9}=(\frac{2}{7}c)^{-6+(-9)}=(\frac{2}{7}c)^{-15}=(\frac{7}{2}\frac{1}{c})^{15}\left[=\frac{4747561509943}{32768} \frac{1}{c^{15}}\right]=\text{ZRM}\)
12. \((\frac{3}{4}y)^{-9}.(\frac{3}{4}y)^{2}=(\frac{3}{4}y)^{-9+2}=(\frac{3}{4}y)^{-7}=(\frac{4}{3}\frac{1}{y})^{7}\left[=\frac{16384}{2187} \frac{1}{y^{7}}\right]=\text{ZRM}\)