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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\left(q^{\frac{1}{5}}\right)^{\frac{-5}{3}}\\= q^{ \frac{1}{5} . (\frac{-5}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
  2. \(\left(a^{-1}\right)^{\frac{3}{5}}\\= a^{ -1 . \frac{3}{5} }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
  3. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-4}{5} . (\frac{-3}{2}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
  4. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-3}{5} . (\frac{-1}{2}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
  5. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-5}{6} . (\frac{-1}{2}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
  6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
  7. \(\left(y^{1}\right)^{\frac{-1}{2}}\\= y^{ 1 . (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
  8. \(\left(a^{-1}\right)^{\frac{1}{2}}\\= a^{ -1 . \frac{1}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
  9. \(\left(y^{\frac{-1}{4}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{4} . \frac{1}{3} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
  10. \(\left(x^{\frac{-4}{5}}\right)^{\frac{1}{5}}\\= x^{ \frac{-4}{5} . \frac{1}{5} }= x^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ x^{4} }}=\frac{1}{\sqrt[25]{ x^{4} }}. \color{purple}{\frac{\sqrt[25]{ x^{21} }}{\sqrt[25]{ x^{21} }}} \\=\frac{\sqrt[25]{ x^{21} }}{x}\\---------------\)
  11. \(\left(a^{\frac{-3}{5}}\right)^{2}\\= a^{ \frac{-3}{5} . 2 }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
  12. \(\left(x^{\frac{-3}{4}}\right)^{-1}\\= x^{ \frac{-3}{4} . (-1) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-03-28 11:37:40