Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{5}{2}}}\\= a^{ 1 - \frac{5}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{5}{6}}}\\= a^{ 1 - \frac{5}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
4. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-3}{4} - \frac{5}{4} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{3}{5} - \frac{2}{3} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
6. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{2}{5} - (\frac{-1}{6}) }= x^{\frac{17}{30}}\\=\sqrt[30]{ x^{17} }\\---------------\)
7. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{3}{4} - (\frac{-3}{4}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
8. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-5}{2} - (\frac{-4}{5}) }= q^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{7} }}=\frac{1}{|q|.\sqrt[10]{ q^{7} }} \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-2}{3} - \frac{4}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
11. \(\dfrac{a^{2}}{a^{1}}\\= a^{ 2 - 1 }= a^{1}\\\\---------------\)
12. \(\dfrac{y^{\frac{2}{3}}}{y^{1}}\\= y^{ \frac{2}{3} - 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)