Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{1}{3} - \frac{2}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
2. \(\dfrac{q^{\frac{-3}{5}}}{q^{-1}}\\= q^{ \frac{-3}{5} - (-1) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{3} - \frac{2}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
4. \(\dfrac{q^{-2}}{q^{\frac{-5}{3}}}\\= q^{ -2 - (\frac{-5}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
5. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{6} - \frac{2}{5} }= y^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ y^{7} }}=\frac{1}{\sqrt[30]{ y^{7} }}. \color{purple}{\frac{\sqrt[30]{ y^{23} }}{\sqrt[30]{ y^{23} }}} \\=\frac{\sqrt[30]{ y^{23} }}{|y|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{4} - (\frac{-1}{2}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{1}}\\= y^{ \frac{-1}{2} - 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{2} - (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{x^{\frac{5}{3}}}{x^{1}}\\= x^{ \frac{5}{3} - 1 }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
11. \(\dfrac{q^{\frac{1}{6}}}{q^{1}}\\= q^{ \frac{1}{6} - 1 }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{-1}}\\= y^{ \frac{-1}{2} - (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)