Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{4}{5} - \frac{1}{2} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
2. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-5}{4} - (\frac{-1}{5}) }= y^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ y^{21} }}\\=\frac{1}{|y|.\sqrt[20]{ y }}=\frac{1}{|y|.\sqrt[20]{ y }} \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{1}{3} - \frac{5}{4} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
4. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{5} - (\frac{-2}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
5. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-5}{4} - \frac{4}{5} }= y^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ y^{41} }}\\=\frac{1}{|y^{2}|.\sqrt[20]{ y }}=\frac{1}{|y^{2}|.\sqrt[20]{ y }} \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y^{3}|}\\---------------\)
6. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
7. \(\dfrac{x^{-2}}{x^{\frac{1}{2}}}\\= x^{ -2 - \frac{1}{2} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
8. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{2} - \frac{2}{3} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{2}}\\= a^{ \frac{1}{2} - 2 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{1}{6}}}\\= y^{ -1 - \frac{1}{6} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{5}}}\\= x^{ \frac{3}{4} - \frac{1}{5} }= x^{\frac{11}{20}}\\=\sqrt[20]{ x^{11} }\\---------------\)