Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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