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Werk uit m.b.v. de rekenregels

  1. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{3}}\)
  2. \(\left(y^{1}\right)^{-1}\)
  3. \(\left(q^{1}\right)^{\frac{2}{3}}\)
  4. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-4}{5}}\)
  5. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{6}}\)
  6. \(\left(x^{\frac{-1}{4}}\right)^{\frac{5}{3}}\)
  7. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{3}}\)
  8. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\)
  9. \(\left(y^{\frac{-1}{5}}\right)^{\frac{5}{3}}\)
  10. \(\left(x^{\frac{4}{5}}\right)^{\frac{-1}{2}}\)
  11. \(\left(x^{\frac{4}{5}}\right)^{\frac{2}{3}}\)
  12. \(\left(q^{\frac{1}{5}}\right)^{\frac{1}{4}}\)

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{4} . (\frac{-1}{3}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
  2. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
  3. \(\left(q^{1}\right)^{\frac{2}{3}}\\= q^{ 1 . \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
  4. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-1}{6} . (\frac{-4}{5}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
  5. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{5}{3} . \frac{1}{6} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
  6. \(\left(x^{\frac{-1}{4}}\right)^{\frac{5}{3}}\\= x^{ \frac{-1}{4} . \frac{5}{3} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
  7. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{1}{2} . \frac{1}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
  8. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
  9. \(\left(y^{\frac{-1}{5}}\right)^{\frac{5}{3}}\\= y^{ \frac{-1}{5} . \frac{5}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
  10. \(\left(x^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{4}{5} . (\frac{-1}{2}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
  11. \(\left(x^{\frac{4}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{4}{5} . \frac{2}{3} }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
  12. \(\left(q^{\frac{1}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{1}{5} . \frac{1}{4} }= q^{\frac{1}{20}}\\=\sqrt[20]{ q }\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-19 17:35:42
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