Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{4}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{6}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(\dfrac{q^{\frac{1}{6}}}{q^{-1}}\\= q^{ \frac{1}{6} - (-1) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{-2}{3}}}{a^{1}}\\= a^{ \frac{-2}{3} - 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{2}{5} - (\frac{-1}{6}) }= x^{\frac{17}{30}}\\=\sqrt[30]{ x^{17} }\\---------------\)
6. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-4}{5} - \frac{1}{2} }= x^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{3} }}=\frac{1}{|x|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{4}{3}}}\\= q^{ \frac{5}{6} - \frac{4}{3} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{-4}{5}}}\\= q^{ -1 - (\frac{-4}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
9. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{2}{3} - \frac{4}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
10. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-5}{4} - \frac{1}{6} }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{2} - \frac{1}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)