Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{1}{4} - (\frac{-5}{3}) }= q^{\frac{23}{12}}\\=\sqrt[12]{ q^{23} }=|q|.\sqrt[12]{ q^{11} }\\---------------\)
2. \(\dfrac{y^{\frac{-1}{3}}}{y^{2}}\\= y^{ \frac{-1}{3} - 2 }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
3. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{6} - \frac{1}{2} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
4. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
5. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-5}{3} - (\frac{-1}{2}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{4}{5} - (\frac{-5}{6}) }= y^{\frac{49}{30}}\\=\sqrt[30]{ y^{49} }=|y|.\sqrt[30]{ y^{19} }\\---------------\)
7. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{5}{6}}}\\= y^{ \frac{1}{6} - \frac{5}{6} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{1}{2} - (\frac{-3}{5}) }= q^{\frac{11}{10}}\\=\sqrt[10]{ q^{11} }=|q|.\sqrt[10]{ q }\\---------------\)
9. \(\dfrac{y^{2}}{y^{\frac{-1}{2}}}\\= y^{ 2 - (\frac{-1}{2}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
10. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{5}{4} - (\frac{-1}{4}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
11. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{3} - \frac{4}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
12. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{4}) }= q^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ q^{7} }}=\frac{1}{\sqrt[20]{ q^{7} }}. \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q|}\\---------------\)