Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-4}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{1}{3}}}\\= y^{ \frac{1}{6} - \frac{1}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{-2}{5}}}\\= a^{ -1 - (\frac{-2}{5}) }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{2}}}{a^{1}}\\= a^{ \frac{-3}{2} - 1 }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
5. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-3}{5} - (\frac{-1}{2}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
6. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{5}{4} - (\frac{-4}{5}) }= a^{\frac{41}{20}}\\=\sqrt[20]{ a^{41} }=|a^{2}|.\sqrt[20]{ a }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{6}}}{x^{1}}\\= x^{ \frac{-1}{6} - 1 }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{1}{2} - \frac{4}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-1}{2} - \frac{3}{5} }= x^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[10]{ x }}=\frac{1}{|x|.\sqrt[10]{ x }} \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{5} - (\frac{-5}{2}) }= y^{\frac{23}{10}}\\=\sqrt[10]{ y^{23} }=|y^{2}|.\sqrt[10]{ y^{3} }\\---------------\)
11. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{1}{4}}}\\= a^{ \frac{4}{3} - \frac{1}{4} }= a^{\frac{13}{12}}\\=\sqrt[12]{ a^{13} }=|a|.\sqrt[12]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{2} - \frac{2}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)