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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\left(x^{\frac{5}{2}}\right)^{\frac{3}{2}}\\= x^{ \frac{5}{2} . \frac{3}{2} }= x^{\frac{15}{4}}\\=\sqrt[4]{ x^{15} }=|x^{3}|.\sqrt[4]{ x^{3} }\\---------------\)
  2. \(\left(x^{\frac{-4}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{-4}{3} . \frac{2}{3} }= x^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ x^{8} }}=\frac{1}{\sqrt[9]{ x^{8} }}. \color{purple}{\frac{\sqrt[9]{ x }}{\sqrt[9]{ x }}} \\=\frac{\sqrt[9]{ x }}{x}\\---------------\)
  3. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-1}{3} . (\frac{-1}{3}) }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
  4. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{4}{3} . \frac{1}{6} }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)
  5. \(\left(x^{\frac{-1}{2}}\right)^{\frac{3}{2}}\\= x^{ \frac{-1}{2} . \frac{3}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
  6. \(\left(x^{\frac{1}{2}}\right)^{\frac{-3}{2}}\\= x^{ \frac{1}{2} . (\frac{-3}{2}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
  7. \(\left(a^{\frac{4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{4}{3} . \frac{2}{3} }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
  8. \(\left(a^{\frac{5}{6}}\right)^{\frac{-3}{5}}\\= a^{ \frac{5}{6} . (\frac{-3}{5}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
  9. \(\left(y^{\frac{2}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{2}{5} . \frac{2}{5} }= y^{\frac{4}{25}}\\=\sqrt[25]{ y^{4} }\\---------------\)
  10. \(\left(y^{1}\right)^{\frac{3}{2}}\\= y^{ 1 . \frac{3}{2} }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
  11. \(\left(y^{\frac{1}{4}}\right)^{2}\\= y^{ \frac{1}{4} . 2 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
  12. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-2}{3} . \frac{1}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-19 06:31:39
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