Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{2} - \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{1}{2} - \frac{5}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-5}{4}}}{q^{1}}\\= q^{ \frac{-5}{4} - 1 }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{5}{2}}}\\= a^{ 1 - \frac{5}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{2} - \frac{3}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{6}}}\\= q^{ \frac{5}{3} - \frac{1}{6} }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
8. \(\dfrac{x^{\frac{-4}{5}}}{x^{1}}\\= x^{ \frac{-4}{5} - 1 }= x^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ x^{9} }}\\=\frac{1}{x.\sqrt[5]{ x^{4} }}=\frac{1}{x.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{2}}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{2}) }= q^{2}\\\\---------------\)
10. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{4}{3} - \frac{3}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-4}{5} - \frac{1}{3} }= x^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ x^{17} }}\\=\frac{1}{x.\sqrt[15]{ x^{2} }}=\frac{1}{x.\sqrt[15]{ x^{2} }} \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{4}{5}}}\\= y^{ \frac{2}{5} - \frac{4}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)