Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{4}}}{x^{1}}\\= x^{ \frac{-1}{4} - 1 }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{-4}{5}}}\\= q^{ 1 - (\frac{-4}{5}) }= q^{\frac{9}{5}}\\=\sqrt[5]{ q^{9} }=q.\sqrt[5]{ q^{4} }\\---------------\)
3. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-5}{4} - \frac{1}{3} }= q^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{7} }}=\frac{1}{|q|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{2}{5}}}\\= x^{ -1 - \frac{2}{5} }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{3}{4}}}\\= q^{ \frac{2}{5} - \frac{3}{4} }= q^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ q^{7} }}=\frac{1}{\sqrt[20]{ q^{7} }}. \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q|}\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{3}{5} - (\frac{-2}{3}) }= a^{\frac{19}{15}}\\=\sqrt[15]{ a^{19} }=a.\sqrt[15]{ a^{4} }\\---------------\)
7. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-3}{4} - \frac{1}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{2}}\\= a^{ \frac{1}{2} - 2 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{1}{3} - \frac{3}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
10. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{5}{6} - (\frac{-3}{5}) }= q^{\frac{43}{30}}\\=\sqrt[30]{ q^{43} }=|q|.\sqrt[30]{ q^{13} }\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{-3}{2}}}\\= q^{ -1 - (\frac{-3}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
12. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-2}{5} - \frac{5}{2} }= a^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ a^{29} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a^{9} }}=\frac{1}{|a^{2}|.\sqrt[10]{ a^{9} }} \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a^{3}|}\\---------------\)