Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-1}{2} - \frac{2}{5} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{1}{6} - (\frac{-5}{2}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{4}{5} - \frac{5}{4} }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
4. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{2}{3} - \frac{5}{6} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{3}{4}}}\\= y^{ \frac{1}{5} - \frac{3}{4} }= y^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ y^{11} }}=\frac{1}{\sqrt[20]{ y^{11} }}. \color{purple}{\frac{\sqrt[20]{ y^{9} }}{\sqrt[20]{ y^{9} }}} \\=\frac{\sqrt[20]{ y^{9} }}{|y|}\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{2} - \frac{5}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{q^{1}}{q^{-1}}\\= q^{ 1 - (-1) }= q^{2}\\\\---------------\)
9. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{1}{6}}}\\= x^{ \frac{4}{3} - \frac{1}{6} }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
10. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
11. \(\dfrac{y^{\frac{1}{3}}}{y^{-1}}\\= y^{ \frac{1}{3} - (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{5}{2}}}\\= y^{ -1 - \frac{5}{2} }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)