Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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