Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{4}{5}}}{q^{-2}}\\= q^{ \frac{4}{5} - (-2) }= q^{\frac{14}{5}}\\=\sqrt[5]{ q^{14} }=q^{2}.\sqrt[5]{ q^{4} }\\---------------\)
2. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-2}{3}) }= x^{0}\\=1\\---------------\)
3. \(\dfrac{y^{\frac{-1}{6}}}{y^{1}}\\= y^{ \frac{-1}{6} - 1 }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{5}}}{y^{1}}\\= y^{ \frac{1}{5} - 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
5. \(\dfrac{q^{1}}{q^{\frac{-5}{3}}}\\= q^{ 1 - (\frac{-5}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{2}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
7. \(\dfrac{a^{2}}{a^{\frac{4}{3}}}\\= a^{ 2 - \frac{4}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-3}{2} - \frac{3}{5} }= x^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ x^{21} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x }}=\frac{1}{|x^{2}|.\sqrt[10]{ x }} \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x^{3}|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-1}{6} - (\frac{-1}{6}) }= q^{0}\\=1\\---------------\)
10. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{2} - \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-3}{2}}}\\= x^{ 1 - (\frac{-3}{2}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
12. \(\dfrac{x^{2}}{x^{\frac{-2}{3}}}\\= x^{ 2 - (\frac{-2}{3}) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)