Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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