Rekenregels machten

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

1. \((\frac{11}{12}b)^{1}.(\frac{11}{12}b)^{1}\)
2. \((\frac{13}{14})^{9}.(\frac{16}{11})^{9}\)
3. \(-(-\frac{4}{5})^{-6}\)
4. \((\frac{17}{20}y)^{6}.(\frac{17}{20}y)^{-5}\)
5. \((\frac{6}{5}b)^{2}:(\frac{6}{5}b)^{-1}\)
6. \((\frac{19}{12})^{-9}.(5)^{-9}\)
7. \((\frac{4}{3}a)^{-7}:(\frac{4}{3}a)^{-2}\)
8. \((2)^{-4}.(\frac{11}{7})^{-4}\)
9. \((\frac{11}{20})^{5}.(\frac{9}{4})^{5}\)
10. \((-\frac{5}{3})^{-3}\)
11. \((\frac{12}{5}c)^{8}:(\frac{12}{5}c)^{-3}\)
12. \((18c^{3})^{2}\)

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

Verbetersleutel

1. \((\frac{11}{12}b)^{1}.(\frac{11}{12}b)^{1}=(\frac{11}{12}b)^{1+1}=(\frac{11}{12}b)^{2}\left[=\frac{121}{144}b^{2}\right]\)
2. \((\frac{13}{14})^{9}.(\frac{16}{11})^{9}=(\frac{13}{14}\frac{16}{11})^{9}=(\frac{104}{77})^{9}=\text{ZRM}=\left[\frac{1423311812421484544}{95151694449171437}\right]\)
3. \(-(-\frac{4}{5})^{-6}=-(-\frac{5}{4})^{6}=-\frac{5^{6}}{4^{6}}=\text{ZRM}\left[=-\frac{15625}{4096}\right]\)
4. \((\frac{17}{20}y)^{6}.(\frac{17}{20}y)^{-5}=(\frac{17}{20}y)^{6+(-5)}=(\frac{17}{20}y)^{1}\left[=\frac{17}{20}y^{1}\right]\)
5. \((\frac{6}{5}b)^{2}:(\frac{6}{5}b)^{-1}=(\frac{6}{5}b)^{2-(-1)}=(\frac{6}{5}b)^{3}=\text{ZRM}\left[ =\frac{216}{125}b^{3} \right]\)
6. \((\frac{19}{12})^{-9}.(5)^{-9}=(\frac{19}{12}5)^{-9}=(\frac{95}{12})^{-9}=(\frac{12}{95})^{9}=\text{ZRM}=\left[\frac{5159780352}{630249409724609375}\right]\)
7. \((\frac{4}{3}a)^{-7}:(\frac{4}{3}a)^{-2}=(\frac{4}{3}a)^{-7-(-2)}=(\frac{4}{3}a)^{-5}=(\frac{3}{4}\frac{1}{a})^{5}=\text{ZRM}\left[ =\frac{243}{1024} \frac{1}{a^{5}} \right]\)
8. \((2)^{-4}.(\frac{11}{7})^{-4}=(2\frac{11}{7})^{-4}=(\frac{22}{7})^{-4}=(\frac{7}{22})^{4}=\text{ZRM}=\left[\frac{2401}{234256}\right]\)
9. \((\frac{11}{20})^{5}.(\frac{9}{4})^{5}=(\frac{11}{20}\frac{9}{4})^{5}=(\frac{99}{80})^{5}=\text{ZRM}=\left[\frac{9509900499}{3276800000}\right]\)
10. \((-\frac{5}{3})^{-3}=(-\frac{3}{5})^{3}=-\frac{3^{3}}{5^{3}}=\text{ZRM}= \left[=-\frac{27}{125}\right]\)
11. \((\frac{12}{5}c)^{8}:(\frac{12}{5}c)^{-3}=(\frac{12}{5}c)^{8-(-3)}=(\frac{12}{5}c)^{11}=\text{ZRM}\left[ =\frac{743008370688}{48828125}c^{11} \right]\)
12. \((18c^{3})^{2}=(18)^{2}.(c^{3})^{2}=\text{ZRM}\left[=324c^{6}\right]\)