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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-5}{2} . (\frac{-5}{3}) }= y^{\frac{25}{6}}\\=\sqrt[6]{ y^{25} }=|y^{4}|.\sqrt[6]{ y }\\---------------\)
  2. \(\left(q^{\frac{3}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{3}{5} . \frac{2}{3} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
  3. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-5}{3} . (\frac{-2}{3}) }= a^{\frac{10}{9}}\\=\sqrt[9]{ a^{10} }=a.\sqrt[9]{ a }\\---------------\)
  4. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
  5. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{1}{2} . (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
  6. \(\left(y^{\frac{3}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{3}{4} . (\frac{-1}{2}) }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
  7. \(\left(q^{\frac{3}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{3}{5} . (\frac{-2}{3}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
  8. \(\left(a^{\frac{-3}{4}}\right)^{\frac{1}{6}}\\= a^{ \frac{-3}{4} . \frac{1}{6} }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
  9. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-3}{5} . (\frac{-1}{4}) }= q^{\frac{3}{20}}\\=\sqrt[20]{ q^{3} }\\---------------\)
  10. \(\left(a^{\frac{-3}{5}}\right)^{2}\\= a^{ \frac{-3}{5} . 2 }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
  11. \(\left(a^{\frac{-2}{5}}\right)^{-1}\\= a^{ \frac{-2}{5} . (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
  12. \(\left(x^{-1}\right)^{\frac{1}{2}}\\= x^{ -1 . \frac{1}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-30 08:54:03
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