Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{6} - (\frac{-2}{3}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
2. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{2}{5} - (\frac{-1}{3}) }= a^{\frac{11}{15}}\\=\sqrt[15]{ a^{11} }\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{2} - \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
4. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{6} - (\frac{-5}{4}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
5. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{4}{3} - \frac{3}{4} }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{3}{5} - \frac{1}{2} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
7. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{4}{3} - \frac{5}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
8. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{2}{5} - \frac{2}{3} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
9. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-5}{6} - (\frac{-1}{3}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{6} - \frac{1}{5} }= y^{\frac{-11}{30}}\\=\frac{1}{\sqrt[30]{ y^{11} }}=\frac{1}{\sqrt[30]{ y^{11} }}. \color{purple}{\frac{\sqrt[30]{ y^{19} }}{\sqrt[30]{ y^{19} }}} \\=\frac{\sqrt[30]{ y^{19} }}{|y|}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{1}{5} - \frac{2}{3} }= y^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ y^{7} }}=\frac{1}{\sqrt[15]{ y^{7} }}. \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y}\\---------------\)