Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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