Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{5}{4}}}\\= a^{ \frac{5}{6} - \frac{5}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{-3}{4}}}{q^{2}}\\= q^{ \frac{-3}{4} - 2 }= q^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ q^{11} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{3}|}\\---------------\)
3. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{3}{5} - (\frac{-3}{2}) }= q^{\frac{21}{10}}\\=\sqrt[10]{ q^{21} }=|q^{2}|.\sqrt[10]{ q }\\---------------\)
4. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-5}{3} - (\frac{-1}{6}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-1}{6}}}{q^{1}}\\= q^{ \frac{-1}{6} - 1 }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{3}{5} - (\frac{-5}{6}) }= x^{\frac{43}{30}}\\=\sqrt[30]{ x^{43} }=|x|.\sqrt[30]{ x^{13} }\\---------------\)
7. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{1}{3} - \frac{3}{5} }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
8. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{1}{4}}}\\= q^{ \frac{1}{5} - \frac{1}{4} }= q^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ q }}=\frac{1}{\sqrt[20]{ q }}. \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q|}\\---------------\)
9. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{5} - \frac{2}{3} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
10. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-2}{5} - \frac{1}{6} }= q^{\frac{-17}{30}}\\=\frac{1}{\sqrt[30]{ q^{17} }}=\frac{1}{\sqrt[30]{ q^{17} }}. \color{purple}{\frac{\sqrt[30]{ q^{13} }}{\sqrt[30]{ q^{13} }}} \\=\frac{\sqrt[30]{ q^{13} }}{|q|}\\---------------\)
11. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{3} - \frac{2}{3} }= q^{0}\\=1\\---------------\)
12. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{5} - \frac{1}{2} }= q^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ q^{7} }}=\frac{1}{\sqrt[10]{ q^{7} }}. \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q|}\\---------------\)