Macht van een macht

Hoofdmenu Eentje per keer 

Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\left(q^{1}\right)^{\frac{4}{5}}\\= q^{ 1 . \frac{4}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
  2. \(\left(a^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= a^{ \frac{1}{2} . (\frac{-5}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
  3. \(\left(q^{\frac{-1}{4}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{4} . \frac{5}{6} }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
  4. \(\left(a^{\frac{3}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{3}{5} . (\frac{-1}{2}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
  5. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-4}{5} . (\frac{-3}{5}) }= a^{\frac{12}{25}}\\=\sqrt[25]{ a^{12} }\\---------------\)
  6. \(\left(q^{-2}\right)^{\frac{3}{2}}\\= q^{ -2 . \frac{3}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
  7. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{-1}{3} . \frac{1}{5} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
  8. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-3}{4} . (\frac{-4}{3}) }= y^{1}\\\\---------------\)
  9. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-5}{3} . (\frac{-1}{3}) }= y^{\frac{5}{9}}\\=\sqrt[9]{ y^{5} }\\---------------\)
  10. \(\left(q^{\frac{3}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{3}{2} . \frac{1}{6} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
  11. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-5}{6} . (\frac{-1}{4}) }= x^{\frac{5}{24}}\\=\sqrt[24]{ x^{5} }\\---------------\)
  12. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-4}{5} . (\frac{-1}{6}) }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-29 15:06:10
Een site van Busleyden Atheneum Mechelen