Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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