Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{6} - (\frac{-1}{2}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
2. \(\dfrac{x^{-1}}{x^{-2}}\\= x^{ -1 - (-2) }= x^{1}\\\\---------------\)
3. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-4}{3} - \frac{1}{4} }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-1}{5} - \frac{5}{3} }= x^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ x^{28} }}\\=\frac{1}{x.\sqrt[15]{ x^{13} }}=\frac{1}{x.\sqrt[15]{ x^{13} }} \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{6}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{5} - (\frac{-1}{3}) }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
7. \(\dfrac{a^{\frac{3}{4}}}{a^{-1}}\\= a^{ \frac{3}{4} - (-1) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
8. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{3} - \frac{5}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{5}{4}}}\\= q^{ \frac{2}{5} - \frac{5}{4} }= q^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ q^{17} }}=\frac{1}{\sqrt[20]{ q^{17} }}. \color{purple}{\frac{\sqrt[20]{ q^{3} }}{\sqrt[20]{ q^{3} }}} \\=\frac{\sqrt[20]{ q^{3} }}{|q|}\\---------------\)
10. \(\dfrac{q^{\frac{-4}{3}}}{q^{-1}}\\= q^{ \frac{-4}{3} - (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
11. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{2}{5}}}\\= q^{ \frac{5}{4} - \frac{2}{5} }= q^{\frac{17}{20}}\\=\sqrt[20]{ q^{17} }\\---------------\)
12. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{5} - (\frac{-1}{2}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)