Rekenregels machten

Hoofdmenu Eentje per keer  🖨

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

1. \((-17y^{8})^{-6}\)
2. \((-\frac{12}{7})^{-6}\)
3. \((-5c^{5})^{-6}\)
4. \((12y^{3})^{-10}\)
5. \(-(-\frac{2}{9})^{-6}\)
6. \((2c^{2})^{4}\)
7. \((\frac{15}{7}y)^{-7}:(\frac{15}{7}y)^{2}\)
8. \((\frac{2}{3}c)^{7}.(\frac{2}{3}c)^{3}\)
9. \((\frac{7}{9})^{2}.(\frac{5}{12})^{2}\)
10. \(-(-\frac{2}{15})^{-3}\)
11. \((\frac{7}{18})^{-3}.(\frac{7}{12})^{-3}\)
12. \((-11a^{7})^{2}\)

---

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

Verbetersleutel

1. \((-17y^{8})^{-6}=(-17)^{-6}.(y^{8})^{-6}=(\frac{1}{-17})^{6}.(\frac{1}{y^{8}})^{6}=\text{ZRM}\left[=\frac{1}{24137569} \frac{1}{y^{48}}\right]\)
2. \((-\frac{12}{7})^{-6}=(-\frac{7}{12})^{6}=+\frac{7^{6}}{12^{6}}=\text{ZRM}= \left[=\frac{117649}{2985984}\right]\)
3. \((-5c^{5})^{-6}=(-5)^{-6}.(c^{5})^{-6}=(\frac{1}{-5})^{6}.(\frac{1}{c^{5}})^{6}=\text{ZRM}\left[=\frac{1}{15625} \frac{1}{c^{30}}\right]\)
4. \((12y^{3})^{-10}=(12)^{-10}.(y^{3})^{-10}=(\frac{1}{12})^{10}.(\frac{1}{y^{3}})^{10}=\text{ZRM}\left[=\frac{1}{61917364224} \frac{1}{y^{30}}\right]\)
5. \(-(-\frac{2}{9})^{-6}=-(-\frac{9}{2})^{6}=-\frac{9^{6}}{2^{6}}=\text{ZRM}\left[=-\frac{531441}{64}\right]\)
6. \((2c^{2})^{4}=(2)^{4}.(c^{2})^{4}=\text{ZRM}\left[=16c^{8}\right]\)
7. \((\frac{15}{7}y)^{-7}:(\frac{15}{7}y)^{2}=(\frac{15}{7}y)^{-7-2}=(\frac{15}{7}y)^{-9}=(\frac{7}{15}\frac{1}{y})^{9}=\text{ZRM}\left[ =\frac{40353607}{38443359375} \frac{1}{y^{9}} \right]\)
8. \((\frac{2}{3}c)^{7}.(\frac{2}{3}c)^{3}=(\frac{2}{3}c)^{7+3}=(\frac{2}{3}c)^{10}\left[=\frac{1024}{59049}c^{10}\right]=\text{ZRM}\)
9. \((\frac{7}{9})^{2}.(\frac{5}{12})^{2}=(\frac{7}{9}\frac{5}{12})^{2}=(\frac{35}{108})^{2}=\left[\frac{1225}{11664}\right]\)
10. \(-(-\frac{2}{15})^{-3}=-(-\frac{15}{2})^{3}=+\frac{15^{3}}{2^{3}}=\text{ZRM}\left[=\frac{3375}{8}\right]\)
11. \((\frac{7}{18})^{-3}.(\frac{7}{12})^{-3}=(\frac{7}{18}\frac{7}{12})^{-3}=(\frac{49}{216})^{-3}=(\frac{216}{49})^{3}=\text{ZRM}=\left[\frac{10077696}{117649}\right]\)
12. \((-11a^{7})^{2}=(-11)^{2}.(a^{7})^{2}=\text{ZRM}\left[=121a^{14}\right]\)