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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(y^{\frac{-3}{5}}.y^{\frac{-4}{3}}\\= y^{ \frac{-3}{5} + (\frac{-4}{3}) }= y^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ y^{29} }}\\=\frac{1}{y.\sqrt[15]{ y^{14} }}=\frac{1}{y.\sqrt[15]{ y^{14} }} \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y^{2}}\\---------------\)
  2. \(a^{\frac{4}{3}}.a^{\frac{4}{3}}\\= a^{ \frac{4}{3} + \frac{4}{3} }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
  3. \(x^{\frac{-2}{3}}.x^{\frac{5}{6}}\\= x^{ \frac{-2}{3} + \frac{5}{6} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
  4. \(y^{\frac{1}{6}}.y^{\frac{1}{5}}\\= y^{ \frac{1}{6} + \frac{1}{5} }= y^{\frac{11}{30}}\\=\sqrt[30]{ y^{11} }\\---------------\)
  5. \(y^{\frac{-1}{2}}.y^{1}\\= y^{ \frac{-1}{2} + 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
  6. \(q^{\frac{-3}{5}}.q^{\frac{-3}{4}}\\= q^{ \frac{-3}{5} + (\frac{-3}{4}) }= q^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ q^{27} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{7} }}=\frac{1}{|q|.\sqrt[20]{ q^{7} }} \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q^{2}|}\\---------------\)
  7. \(x^{\frac{1}{2}}.x^{\frac{5}{2}}\\= x^{ \frac{1}{2} + \frac{5}{2} }= x^{3}\\\\---------------\)
  8. \(y^{\frac{1}{3}}.y^{\frac{2}{3}}\\= y^{ \frac{1}{3} + \frac{2}{3} }= y^{1}\\\\---------------\)
  9. \(y^{\frac{2}{3}}.y^{\frac{1}{5}}\\= y^{ \frac{2}{3} + \frac{1}{5} }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
  10. \(a^{\frac{4}{3}}.a^{1}\\= a^{ \frac{4}{3} + 1 }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
  11. \(y^{\frac{-1}{5}}.y^{\frac{3}{4}}\\= y^{ \frac{-1}{5} + \frac{3}{4} }= y^{\frac{11}{20}}\\=\sqrt[20]{ y^{11} }\\---------------\)
  12. \(x^{1}.x^{\frac{5}{4}}\\= x^{ 1 + \frac{5}{4} }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-03-28 21:13:29