Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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