Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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