Macht van een macht

Hoofdmenu Eentje per keer 

Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\left(y^{\frac{-3}{2}}\right)^{-1}\\= y^{ \frac{-3}{2} . (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
  2. \(\left(a^{-1}\right)^{2}\\= a^{ -1 . 2 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
  3. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
  4. \(\left(x^{1}\right)^{\frac{-5}{6}}\\= x^{ 1 . (\frac{-5}{6}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
  5. \(\left(a^{\frac{-5}{3}}\right)^{1}\\= a^{ \frac{-5}{3} . 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
  6. \(\left(q^{\frac{1}{6}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{6} . (\frac{-4}{3}) }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
  7. \(\left(y^{\frac{-1}{3}}\right)^{-1}\\= y^{ \frac{-1}{3} . (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
  8. \(\left(y^{\frac{-1}{6}}\right)^{\frac{5}{3}}\\= y^{ \frac{-1}{6} . \frac{5}{3} }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
  9. \(\left(a^{\frac{5}{2}}\right)^{\frac{-2}{3}}\\= a^{ \frac{5}{2} . (\frac{-2}{3}) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
  10. \(\left(a^{1}\right)^{\frac{1}{2}}\\= a^{ 1 . \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
  11. \(\left(a^{\frac{3}{5}}\right)^{1}\\= a^{ \frac{3}{5} . 1 }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
  12. \(\left(x^{\frac{-5}{3}}\right)^{\frac{5}{6}}\\= x^{ \frac{-5}{3} . \frac{5}{6} }= x^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ x^{25} }}\\=\frac{1}{|x|.\sqrt[18]{ x^{7} }}=\frac{1}{|x|.\sqrt[18]{ x^{7} }} \color{purple}{\frac{\sqrt[18]{ x^{11} }}{\sqrt[18]{ x^{11} }}} \\=\frac{\sqrt[18]{ x^{11} }}{|x^{2}|}\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-16 19:36:23
Een site van Busleyden Atheneum Mechelen