Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-5}{2} - \frac{5}{6} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{-1}}\\= x^{ \frac{-1}{3} - (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{1}{5} - (\frac{-5}{2}) }= y^{\frac{27}{10}}\\=\sqrt[10]{ y^{27} }=|y^{2}|.\sqrt[10]{ y^{7} }\\---------------\)
4. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-4}{3} - \frac{2}{3} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-3}{5} - \frac{5}{6} }= y^{\frac{-43}{30}}\\=\frac{1}{\sqrt[30]{ y^{43} }}\\=\frac{1}{|y|.\sqrt[30]{ y^{13} }}=\frac{1}{|y|.\sqrt[30]{ y^{13} }} \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{4}{3} - \frac{5}{2} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{3} - \frac{1}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
10. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{3}{2} - (\frac{-1}{3}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
11. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{4} - \frac{1}{2} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{5} - \frac{5}{4} }= q^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ q^{29} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{9} }}=\frac{1}{|q|.\sqrt[20]{ q^{9} }} \color{purple}{\frac{\sqrt[20]{ q^{11} }}{\sqrt[20]{ q^{11} }}} \\=\frac{\sqrt[20]{ q^{11} }}{|q^{2}|}\\---------------\)