Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-1}{5} - (\frac{-2}{3}) }= x^{\frac{7}{15}}\\=\sqrt[15]{ x^{7} }\\---------------\)
2. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-2}{3} - \frac{5}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
3. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{2}{3} - \frac{1}{2} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{6}) }= x^{0}\\=1\\---------------\)
5. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{3}{4}}}\\= a^{ \frac{1}{6} - \frac{3}{4} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-2}{5} - \frac{1}{3} }= a^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ a^{11} }}=\frac{1}{\sqrt[15]{ a^{11} }}. \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a}\\---------------\)
7. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{6}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-1}{6} - \frac{4}{3} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{3}{2} - (\frac{-4}{5}) }= x^{\frac{23}{10}}\\=\sqrt[10]{ x^{23} }=|x^{2}|.\sqrt[10]{ x^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{2}{5}}}\\= q^{ \frac{2}{5} - \frac{2}{5} }= q^{0}\\=1\\---------------\)
11. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{4}{3}}}\\= a^{ \frac{5}{6} - \frac{4}{3} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{2}{3} - \frac{1}{4} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)