Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{5}{6} - (\frac{-1}{2}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
2. \(\dfrac{a^{\frac{1}{6}}}{a^{1}}\\= a^{ \frac{1}{6} - 1 }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
3. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{4}{5} - (\frac{-1}{2}) }= a^{\frac{13}{10}}\\=\sqrt[10]{ a^{13} }=|a|.\sqrt[10]{ a^{3} }\\---------------\)
4. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{6} - (\frac{-2}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-1}{5} - \frac{3}{5} }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
6. \(\dfrac{a^{-2}}{a^{\frac{1}{2}}}\\= a^{ -2 - \frac{1}{2} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
7. \(\dfrac{x^{\frac{1}{3}}}{x^{-1}}\\= x^{ \frac{1}{3} - (-1) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-1}{5} - \frac{5}{4} }= a^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ a^{29} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{9} }}=\frac{1}{|a|.\sqrt[20]{ a^{9} }} \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
10. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{4}{5}}}\\= a^{ \frac{1}{4} - \frac{4}{5} }= a^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ a^{11} }}=\frac{1}{\sqrt[20]{ a^{11} }}. \color{purple}{\frac{\sqrt[20]{ a^{9} }}{\sqrt[20]{ a^{9} }}} \\=\frac{\sqrt[20]{ a^{9} }}{|a|}\\---------------\)
11. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{2} - \frac{2}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{3} - (\frac{-1}{2}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)