Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{1}{3} - (\frac{-5}{2}) }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)
2. \(\dfrac{a^{-2}}{a^{\frac{1}{2}}}\\= a^{ -2 - \frac{1}{2} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{5} - (\frac{-2}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
4. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{4}{3}}}\\= y^{ \frac{2}{5} - \frac{4}{3} }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)
5. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{3} - \frac{2}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
7. \(\dfrac{x^{\frac{1}{6}}}{x^{1}}\\= x^{ \frac{1}{6} - 1 }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{2} - \frac{2}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-5}{3} - (\frac{-5}{6}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\dfrac{x^{1}}{x^{-1}}\\= x^{ 1 - (-1) }= x^{2}\\\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{1}{2} - (\frac{-3}{5}) }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)