Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{-1}{4}}}\\= x^{ 1 - (\frac{-1}{4}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{2} - \frac{2}{3} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{-5}{3}}}\\= y^{ -1 - (\frac{-5}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-1}{3} - \frac{1}{6} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{2} - \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
7. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-5}{2} - \frac{1}{4} }= x^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ x^{11} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x^{3} }}=\frac{1}{|x^{2}|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{3}|}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-1}{3} - \frac{2}{5} }= x^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ x^{11} }}=\frac{1}{\sqrt[15]{ x^{11} }}. \color{purple}{\frac{\sqrt[15]{ x^{4} }}{\sqrt[15]{ x^{4} }}} \\=\frac{\sqrt[15]{ x^{4} }}{x}\\---------------\)
9. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-5}{4} - \frac{5}{6} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{-2}}\\= a^{ \frac{1}{2} - (-2) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{2} - \frac{2}{5} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-4}{5} - (\frac{-5}{2}) }= y^{\frac{17}{10}}\\=\sqrt[10]{ y^{17} }=|y|.\sqrt[10]{ y^{7} }\\---------------\)