Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
2. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{1}{3} - \frac{5}{6} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
3. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-3}{5} - \frac{2}{3} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{1}{3} - \frac{5}{4} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{2}{3} - \frac{3}{4} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
6. \(\dfrac{x^{\frac{2}{5}}}{x^{-1}}\\= x^{ \frac{2}{5} - (-1) }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
7. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{6} - (\frac{-1}{3}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
8. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{3}{4} - (\frac{-5}{6}) }= x^{\frac{19}{12}}\\=\sqrt[12]{ x^{19} }=|x|.\sqrt[12]{ x^{7} }\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
10. \(\dfrac{x^{\frac{1}{4}}}{x^{-2}}\\= x^{ \frac{1}{4} - (-2) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
11. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{2}{3} - \frac{4}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
12. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-5}{6} - (\frac{-1}{4}) }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)