Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-5}{3} - \frac{1}{3} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
2. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-1}{6} - (\frac{-3}{4}) }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
3. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{4}{3} - \frac{2}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{5}{2} - (\frac{-3}{5}) }= y^{\frac{31}{10}}\\=\sqrt[10]{ y^{31} }=|y^{3}|.\sqrt[10]{ y }\\---------------\)
5. \(\dfrac{q^{\frac{5}{2}}}{q^{-1}}\\= q^{ \frac{5}{2} - (-1) }= q^{\frac{7}{2}}\\= \sqrt{ q^{7} } =|q^{3}|. \sqrt{ q } \\---------------\)
6. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{3} - \frac{1}{4} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{-1}{2}}}\\= x^{ -1 - (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{1}{4} - \frac{3}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{5}{3} - (\frac{-1}{2}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
10. \(\dfrac{y^{\frac{1}{4}}}{y^{1}}\\= y^{ \frac{1}{4} - 1 }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{4} - \frac{1}{3} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{1}{2}}}\\= a^{ -1 - \frac{1}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)