Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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