Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
2. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{5}{2} - \frac{3}{5} }= y^{\frac{19}{10}}\\=\sqrt[10]{ y^{19} }=|y|.\sqrt[10]{ y^{9} }\\---------------\)
3. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-3}{4} - \frac{2}{3} }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{-2}{3}}}{q^{-1}}\\= q^{ \frac{-2}{3} - (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
5. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-3}{5} - (\frac{-2}{3}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{1}{4}}}\\= q^{ \frac{2}{5} - \frac{1}{4} }= q^{\frac{3}{20}}\\=\sqrt[20]{ q^{3} }\\---------------\)
7. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{5}{4} - \frac{4}{5} }= y^{\frac{9}{20}}\\=\sqrt[20]{ y^{9} }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{6} - (\frac{-1}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
9. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-3}{5} - (\frac{-3}{2}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{2}{3} - \frac{4}{5} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
11. \(\dfrac{q^{\frac{-5}{2}}}{q^{1}}\\= q^{ \frac{-5}{2} - 1 }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{4}{3}}}\\= y^{ \frac{1}{3} - \frac{4}{3} }= y^{-1}\\=\frac{1}{y}\\---------------\)