Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\\= q^{ \frac{5}{4} - 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{-5}{2}}}\\= q^{ -1 - (\frac{-5}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
3. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-2}{5} - \frac{5}{6} }= y^{\frac{-37}{30}}\\=\frac{1}{\sqrt[30]{ y^{37} }}\\=\frac{1}{|y|.\sqrt[30]{ y^{7} }}=\frac{1}{|y|.\sqrt[30]{ y^{7} }} \color{purple}{\frac{\sqrt[30]{ y^{23} }}{\sqrt[30]{ y^{23} }}} \\=\frac{\sqrt[30]{ y^{23} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-5}{4} - (\frac{-5}{6}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{6}}}{x^{-1}}\\= x^{ \frac{-1}{6} - (-1) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-1}{3} - \frac{5}{2} }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{2} - \frac{2}{5} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-1}{6} - (\frac{-5}{2}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{-1}{2}}}\\= x^{ -1 - (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
11. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{2} - \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)