Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{1}}\\= y^{ \frac{1}{3} - 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
2. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-5}{2} - \frac{5}{3} }= x^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ x^{25} }}\\=\frac{1}{|x^{4}|.\sqrt[6]{ x }}=\frac{1}{|x^{4}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{5}|}\\---------------\)
3. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-4}{3} - (\frac{-5}{6}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{-5}{4}}}\\= a^{ -1 - (\frac{-5}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
5. \(\dfrac{y^{\frac{-4}{3}}}{y^{1}}\\= y^{ \frac{-4}{3} - 1 }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
6. \(\dfrac{x^{\frac{-3}{2}}}{x^{-1}}\\= x^{ \frac{-3}{2} - (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
7. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{6} - (\frac{-5}{2}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{2} - \frac{2}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{2} - \frac{1}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
10. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-3}{2} - \frac{2}{5} }= a^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{9} }}=\frac{1}{|a|.\sqrt[10]{ a^{9} }} \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{3}{5}}}\\= q^{ \frac{-3}{4} - \frac{3}{5} }= q^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ q^{27} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{7} }}=\frac{1}{|q|.\sqrt[20]{ q^{7} }} \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{5}{6}}}\\= y^{ -1 - \frac{5}{6} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)