Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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