Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{3} - (\frac{-1}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{2} - \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
3. \(\dfrac{q^{\frac{5}{3}}}{q^{-1}}\\= q^{ \frac{5}{3} - (-1) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{5}{4}}}{y^{-1}}\\= y^{ \frac{5}{4} - (-1) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{3} - \frac{1}{2} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{1}{5} - \frac{5}{6} }= y^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ y^{19} }}=\frac{1}{\sqrt[30]{ y^{19} }}. \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-5}{3} - (\frac{-4}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{6}}}{a^{1}}\\= a^{ \frac{-1}{6} - 1 }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{6} - \frac{1}{5} }= x^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ x }}=\frac{1}{\sqrt[30]{ x }}. \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x|}\\---------------\)
11. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-5}{2} - \frac{5}{6} }= q^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ q^{10} }}\\=\frac{1}{q^{3}.\sqrt[3]{ q }}=\frac{1}{q^{3}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{4}}\\---------------\)
12. \(\dfrac{y^{\frac{3}{2}}}{y^{-1}}\\= y^{ \frac{3}{2} - (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)