Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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