Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{5}{6} - (\frac{-1}{6}) }= q^{1}\\\\---------------\)
2. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{4}{3} - (\frac{-1}{6}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
3. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{3} - \frac{1}{2} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{2}) }= x^{0}\\=1\\---------------\)
6. \(\dfrac{x^{-2}}{x^{\frac{1}{2}}}\\= x^{ -2 - \frac{1}{2} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
7. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{6}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{3}}}{q^{1}}\\= q^{ \frac{1}{3} - 1 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
9. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{4}}}\\= a^{ \frac{1}{2} - \frac{5}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{5}}}\\= a^{ \frac{2}{3} - \frac{1}{5} }= a^{\frac{7}{15}}\\=\sqrt[15]{ a^{7} }\\---------------\)
11. \(\dfrac{q^{\frac{-5}{3}}}{q^{-1}}\\= q^{ \frac{-5}{3} - (-1) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
12. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-4}{3} - \frac{4}{5} }= y^{\frac{-32}{15}}\\=\frac{1}{\sqrt[15]{ y^{32} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{3}}\\---------------\)