Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{3}{5}}}{q^{1}}\\= q^{ \frac{3}{5} - 1 }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
2. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{2}}\\= y^{ \frac{-1}{3} - 2 }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-4}{5}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
5. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{5} - \frac{2}{3} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{6}}}\\= x^{ \frac{2}{3} - \frac{1}{6} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
7. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{6} - (\frac{-5}{2}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{-3}{5}}}\\= x^{ 1 - (\frac{-3}{5}) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{2} - \frac{4}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{4}}}{y^{-1}}\\= y^{ \frac{-1}{4} - (-1) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
12. \(\dfrac{x^{\frac{-4}{5}}}{x^{1}}\\= x^{ \frac{-4}{5} - 1 }= x^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ x^{9} }}\\=\frac{1}{x.\sqrt[5]{ x^{4} }}=\frac{1}{x.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{2}}\\---------------\)