Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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