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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\left(q^{\frac{-3}{2}}\right)^{\frac{-3}{5}}\\= q^{ \frac{-3}{2} . (\frac{-3}{5}) }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
  2. \(\left(q^{\frac{1}{2}}\right)^{\frac{-4}{5}}\\= q^{ \frac{1}{2} . (\frac{-4}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
  3. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
  4. \(\left(a^{1}\right)^{\frac{1}{5}}\\= a^{ 1 . \frac{1}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
  5. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
  6. \(\left(q^{\frac{1}{5}}\right)^{-2}\\= q^{ \frac{1}{5} . (-2) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
  7. \(\left(q^{\frac{-2}{3}}\right)^{-1}\\= q^{ \frac{-2}{3} . (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
  8. \(\left(y^{\frac{1}{4}}\right)^{2}\\= y^{ \frac{1}{4} . 2 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
  9. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{4}}\\= q^{ \frac{1}{2} . \frac{5}{4} }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
  10. \(\left(q^{-1}\right)^{\frac{3}{5}}\\= q^{ -1 . \frac{3}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
  11. \(\left(a^{\frac{5}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{5}{3} . (\frac{-4}{3}) }= a^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ a^{20} }}\\=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }} \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a^{3}}\\---------------\)
  12. \(\left(a^{\frac{-2}{3}}\right)^{1}\\= a^{ \frac{-2}{3} . 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-25 10:26:04
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