Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{4}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
2. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{5} - (\frac{-1}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{2}{3}}}\\= a^{ 1 - \frac{2}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
4. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{3}{4} - (\frac{-1}{4}) }= y^{1}\\\\---------------\)
5. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{3} - \frac{1}{5} }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
6. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{-2}}\\= a^{ \frac{-1}{2} - (-2) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
8. \(\dfrac{a^{-2}}{a^{\frac{1}{3}}}\\= a^{ -2 - \frac{1}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
9. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-4}{5} - (\frac{-5}{3}) }= q^{\frac{13}{15}}\\=\sqrt[15]{ q^{13} }\\---------------\)
10. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-5}{4} - \frac{5}{6} }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
11. \(\dfrac{y^{\frac{-5}{6}}}{y^{1}}\\= y^{ \frac{-5}{6} - 1 }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-1}{5} - \frac{3}{5} }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)