Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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