Rekenregels machten

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

1. \(-(-\frac{15}{14})^{-1}\)
2. \((\frac{2}{3})^{1}.(\frac{11}{12})^{1}\)
3. \((-\frac{7}{12})^{-5}\)
4. \((8a^{6})^{5}\)
5. \((\frac{9}{7}y)^{-9}:(\frac{9}{7}y)^{-3}\)
6. \((\frac{7}{20}c)^{3}.(\frac{7}{20}c)^{-5}\)
7. \((\frac{3}{4}y)^{-6}.(\frac{3}{4}y)^{-5}\)
8. \((\frac{2}{11}y)^{-5}:(\frac{2}{11}y)^{-4}\)
9. \((\frac{4}{5})^{8}.(\frac{10}{3})^{8}\)
10. \((\frac{5}{2}x)^{9}.(\frac{5}{2}x)^{10}\)
11. \((\frac{13}{20}c)^{-2}.(\frac{13}{20}c)^{2}\)
12. \((-15y^{9})^{8}\)

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

Verbetersleutel

1. \(-(-\frac{15}{14})^{-1}=-(-\frac{14}{15})^{1}=+\frac{14^{1}}{15^{1}}\left[=\frac{14}{15}\right]\)
2. \((\frac{2}{3})^{1}.(\frac{11}{12})^{1}=(\frac{2}{3}\frac{11}{12})^{1}=(\frac{11}{18})^{1}=\left[\frac{11}{18}\right]\)
3. \((-\frac{7}{12})^{-5}=(-\frac{12}{7})^{5}=-\frac{12^{5}}{7^{5}}=\text{ZRM}= \left[=-\frac{248832}{16807}\right]\)
4. \((8a^{6})^{5}=(8)^{5}.(a^{6})^{5}=\text{ZRM}\left[=32768a^{30}\right]\)
5. \((\frac{9}{7}y)^{-9}:(\frac{9}{7}y)^{-3}=(\frac{9}{7}y)^{-9-(-3)}=(\frac{9}{7}y)^{-6}=(\frac{7}{9}\frac{1}{y})^{6}=\text{ZRM}\left[ =\frac{117649}{531441} \frac{1}{y^{6}} \right]\)
6. \((\frac{7}{20}c)^{3}.(\frac{7}{20}c)^{-5}=(\frac{7}{20}c)^{3+(-5)}=(\frac{7}{20}c)^{-2}=(\frac{20}{7}\frac{1}{c})^{2}\left[=\frac{400}{49} \frac{1}{c^{2}}\right]\)
7. \((\frac{3}{4}y)^{-6}.(\frac{3}{4}y)^{-5}=(\frac{3}{4}y)^{-6+(-5)}=(\frac{3}{4}y)^{-11}=(\frac{4}{3}\frac{1}{y})^{11}\left[=\frac{4194304}{177147} \frac{1}{y^{11}}\right]=\text{ZRM}\)
8. \((\frac{2}{11}y)^{-5}:(\frac{2}{11}y)^{-4}=(\frac{2}{11}y)^{-5-(-4)}=(\frac{2}{11}y)^{-1}=(\frac{11}{2}\frac{1}{y})^{1}\left[ =\frac{11}{2} \frac{1}{y^{1}} \right]\)
9. \((\frac{4}{5})^{8}.(\frac{10}{3})^{8}=(\frac{4}{5}\frac{10}{3})^{8}=(\frac{8}{3})^{8}=\text{ZRM}=\left[\frac{16777216}{6561}\right]\)
10. \((\frac{5}{2}x)^{9}.(\frac{5}{2}x)^{10}=(\frac{5}{2}x)^{9+10}=(\frac{5}{2}x)^{19}\left[=\frac{19073486328125}{524288}x^{19}\right]=\text{ZRM}\)
11. \((\frac{13}{20}c)^{-2}.(\frac{13}{20}c)^{2}=(\frac{13}{20}c)^{-2+2}=(\frac{13}{20}c)^{0}\left[=1c^{0}\right]\left[=1\right]\)
12. \((-15y^{9})^{8}=(-15)^{8}.(y^{9})^{8}=\text{ZRM}\left[=2562890625y^{72}\right]\)