Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{4}{5}}}{x^{1}}\\= x^{ \frac{4}{5} - 1 }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{3}{5}}}\\= q^{ \frac{1}{2} - \frac{3}{5} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{a^{\frac{-2}{3}}}{a^{1}}\\= a^{ \frac{-2}{3} - 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-4}{5} - \frac{2}{5} }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{1}{3} - (\frac{-1}{4}) }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
9. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-3}{4} - \frac{3}{5} }= y^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ y^{27} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{7} }}=\frac{1}{|y|.\sqrt[20]{ y^{7} }} \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{-5}{4}}}\\= x^{ 1 - (\frac{-5}{4}) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
11. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{4}{3}}}\\= x^{ \frac{3}{5} - \frac{4}{3} }= x^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ x^{11} }}=\frac{1}{\sqrt[15]{ x^{11} }}. \color{purple}{\frac{\sqrt[15]{ x^{4} }}{\sqrt[15]{ x^{4} }}} \\=\frac{\sqrt[15]{ x^{4} }}{x}\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)