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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\left(y^{1}\right)^{\frac{3}{5}}\\= y^{ 1 . \frac{3}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
  2. \(\left(q^{1}\right)^{\frac{5}{6}}\\= q^{ 1 . \frac{5}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
  3. \(\left(q^{-2}\right)^{\frac{-4}{3}}\\= q^{ -2 . (\frac{-4}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
  4. \(\left(q^{\frac{-2}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{-2}{3} . \frac{5}{6} }= q^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ q^{5} }}=\frac{1}{\sqrt[9]{ q^{5} }}. \color{purple}{\frac{\sqrt[9]{ q^{4} }}{\sqrt[9]{ q^{4} }}} \\=\frac{\sqrt[9]{ q^{4} }}{q}\\---------------\)
  5. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-5}{3} . (\frac{-1}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
  6. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{3} . (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
  7. \(\left(y^{\frac{1}{3}}\right)^{\frac{-5}{3}}\\= y^{ \frac{1}{3} . (\frac{-5}{3}) }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)
  8. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{1}{2} . (\frac{-5}{4}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
  9. \(\left(y^{1}\right)^{\frac{-5}{4}}\\= y^{ 1 . (\frac{-5}{4}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
  10. \(\left(q^{\frac{1}{3}}\right)^{-1}\\= q^{ \frac{1}{3} . (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
  11. \(\left(y^{\frac{-4}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{-4}{5} . \frac{4}{5} }= y^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ y^{16} }}=\frac{1}{\sqrt[25]{ y^{16} }}. \color{purple}{\frac{\sqrt[25]{ y^{9} }}{\sqrt[25]{ y^{9} }}} \\=\frac{\sqrt[25]{ y^{9} }}{y}\\---------------\)
  12. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{1}{3} . \frac{1}{5} }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-17 19:32:52
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