Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{4} - \frac{4}{5} }= a^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ a^{21} }}\\=\frac{1}{|a|.\sqrt[20]{ a }}=\frac{1}{|a|.\sqrt[20]{ a }} \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{3} - \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\dfrac{a^{\frac{-4}{3}}}{a^{1}}\\= a^{ \frac{-4}{3} - 1 }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
4. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{1}{6}}}\\= a^{ \frac{3}{4} - \frac{1}{6} }= a^{\frac{7}{12}}\\=\sqrt[12]{ a^{7} }\\---------------\)
5. \(\dfrac{y^{\frac{1}{5}}}{y^{1}}\\= y^{ \frac{1}{5} - 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
6. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-3}{2} - \frac{2}{5} }= a^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{9} }}=\frac{1}{|a|.\sqrt[10]{ a^{9} }} \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{3}{2} - (\frac{-5}{6}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-1}{6} - (\frac{-4}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{2} - \frac{2}{3} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{2}}\\= a^{ \frac{-1}{3} - 2 }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
11. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-5}{3} - \frac{1}{5} }= x^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ x^{28} }}\\=\frac{1}{x.\sqrt[15]{ x^{13} }}=\frac{1}{x.\sqrt[15]{ x^{13} }} \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x^{2}}\\---------------\)
12. \(\dfrac{a^{2}}{a^{\frac{-1}{5}}}\\= a^{ 2 - (\frac{-1}{5}) }= a^{\frac{11}{5}}\\=\sqrt[5]{ a^{11} }=a^{2}.\sqrt[5]{ a }\\---------------\)