Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-5}{6} - \frac{1}{2} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
2. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{2}{5} - (\frac{-1}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
3. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{5} - \frac{1}{2} }= q^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ q^{7} }}=\frac{1}{\sqrt[10]{ q^{7} }}. \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q|}\\---------------\)
4. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{2} - \frac{4}{5} }= a^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{3} }}=\frac{1}{|a|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-5}{4} - \frac{4}{5} }= x^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ x^{41} }}\\=\frac{1}{|x^{2}|.\sqrt[20]{ x }}=\frac{1}{|x^{2}|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{3}|}\\---------------\)
7. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{5}{3} - (\frac{-5}{2}) }= y^{\frac{25}{6}}\\=\sqrt[6]{ y^{25} }=|y^{4}|.\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-5}{3} - (\frac{-4}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{2} - \frac{5}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-2}{3} - \frac{1}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
11. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{2}{3} - (\frac{-3}{2}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)