Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{6}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{4}) }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{2}{5}}}\\= y^{ -1 - \frac{2}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{6} - (\frac{-2}{5}) }= y^{\frac{17}{30}}\\=\sqrt[30]{ y^{17} }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-1}{5} - \frac{5}{3} }= x^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ x^{28} }}\\=\frac{1}{x.\sqrt[15]{ x^{13} }}=\frac{1}{x.\sqrt[15]{ x^{13} }} \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-2}{5} - \frac{4}{3} }= x^{\frac{-26}{15}}\\=\frac{1}{\sqrt[15]{ x^{26} }}\\=\frac{1}{x.\sqrt[15]{ x^{11} }}=\frac{1}{x.\sqrt[15]{ x^{11} }} \color{purple}{\frac{\sqrt[15]{ x^{4} }}{\sqrt[15]{ x^{4} }}} \\=\frac{\sqrt[15]{ x^{4} }}{x^{2}}\\---------------\)
7. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{3} - (\frac{-1}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{q^{-2}}{q^{\frac{-3}{2}}}\\= q^{ -2 - (\frac{-3}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{4}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
10. \(\dfrac{a^{\frac{1}{3}}}{a^{1}}\\= a^{ \frac{1}{3} - 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
11. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)