Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{6}}}{q^{1}}\\= q^{ \frac{5}{6} - 1 }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{2} - (\frac{-2}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
3. \(\dfrac{x^{\frac{-5}{6}}}{x^{-1}}\\= x^{ \frac{-5}{6} - (-1) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
4. \(\dfrac{x^{1}}{x^{\frac{2}{5}}}\\= x^{ 1 - \frac{2}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
5. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{5}{3} - \frac{5}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-3}{5}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{3}{2} - (\frac{-1}{2}) }= y^{2}\\\\---------------\)
9. \(\dfrac{x^{\frac{3}{2}}}{x^{1}}\\= x^{ \frac{3}{2} - 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{2} - \frac{2}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
12. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-4}{3} - \frac{2}{5} }= y^{\frac{-26}{15}}\\=\frac{1}{\sqrt[15]{ y^{26} }}\\=\frac{1}{y.\sqrt[15]{ y^{11} }}=\frac{1}{y.\sqrt[15]{ y^{11} }} \color{purple}{\frac{\sqrt[15]{ y^{4} }}{\sqrt[15]{ y^{4} }}} \\=\frac{\sqrt[15]{ y^{4} }}{y^{2}}\\---------------\)