Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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