Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{6} - (\frac{-5}{3}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
2. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-2}{3} - \frac{2}{5} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{1}{4}}}\\= x^{ \frac{4}{5} - \frac{1}{4} }= x^{\frac{11}{20}}\\=\sqrt[20]{ x^{11} }\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{1}{2} - (\frac{-5}{3}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{5}{4}}}{q^{-1}}\\= q^{ \frac{5}{4} - (-1) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
7. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{6} - (\frac{-2}{3}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
8. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-3}{5} - (\frac{-5}{2}) }= q^{\frac{19}{10}}\\=\sqrt[10]{ q^{19} }=|q|.\sqrt[10]{ q^{9} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{-2}{5}}}{a^{-1}}\\= a^{ \frac{-2}{5} - (-1) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
11. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{6} - (\frac{-5}{2}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
12. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-1}{2} - \frac{1}{6} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)