Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{-5}{6}}}\\= x^{ -1 - (\frac{-5}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{3}{4}}}\\= q^{ \frac{1}{6} - \frac{3}{4} }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{3}{2}}}\\= x^{ -1 - \frac{3}{2} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
4. \(\dfrac{a^{\frac{-5}{6}}}{a^{-1}}\\= a^{ \frac{-5}{6} - (-1) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{1}{5}}}\\= q^{ \frac{5}{6} - \frac{1}{5} }= q^{\frac{19}{30}}\\=\sqrt[30]{ q^{19} }\\---------------\)
6. \(\dfrac{x^{\frac{4}{5}}}{x^{-1}}\\= x^{ \frac{4}{5} - (-1) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
7. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{3}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
8. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-5}{2} - (\frac{-5}{2}) }= a^{0}\\=1\\---------------\)
9. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-5}{6} - (\frac{-5}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-2}{3} - (\frac{-2}{3}) }= y^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{2}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{2}{3}}}\\= a^{ -1 - \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)