Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{3} - \frac{2}{5} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
2. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{3}) }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
3. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{5}{2}}}\\= x^{ \frac{3}{5} - \frac{5}{2} }= x^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{9} }}=\frac{1}{|x|.\sqrt[10]{ x^{9} }} \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{5} - (\frac{-1}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
5. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{5} - (\frac{-5}{4}) }= y^{\frac{29}{20}}\\=\sqrt[20]{ y^{29} }=|y|.\sqrt[20]{ y^{9} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{6}}}{y^{1}}\\= y^{ \frac{-1}{6} - 1 }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-1}{2} - \frac{2}{5} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{5}{2} - (\frac{-1}{5}) }= x^{\frac{27}{10}}\\=\sqrt[10]{ x^{27} }=|x^{2}|.\sqrt[10]{ x^{7} }\\---------------\)
10. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-2}{5} - (\frac{-2}{5}) }= a^{0}\\=1\\---------------\)
11. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-4}{3} - \frac{1}{6} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{4}}}{a^{1}}\\= a^{ \frac{-1}{4} - 1 }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)