Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-3}{4} - (\frac{-4}{5}) }= q^{\frac{1}{20}}\\=\sqrt[20]{ q }\\---------------\)
2. \(\dfrac{a^{-2}}{a^{\frac{3}{2}}}\\= a^{ -2 - \frac{3}{2} }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
3. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{3}{5}}}\\= x^{ \frac{3}{4} - \frac{3}{5} }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
4. \(\dfrac{q^{\frac{1}{6}}}{q^{1}}\\= q^{ \frac{1}{6} - 1 }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{1}{6}}}\\= y^{ -1 - \frac{1}{6} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-1}{5}}}\\= x^{ 1 - (\frac{-1}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{1}{2} - (\frac{-5}{6}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
8. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{2} - \frac{1}{2} }= q^{2}\\\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{-5}{2}}}\\= x^{ 1 - (\frac{-5}{2}) }= x^{\frac{7}{2}}\\= \sqrt{ x^{7} } =|x^{3}|. \sqrt{ x } \\---------------\)
10. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{2}{3} - \frac{2}{5} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
11. \(\dfrac{a^{-1}}{a^{\frac{2}{3}}}\\= a^{ -1 - \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{4}{5} - \frac{5}{4} }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)