Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{4}{3}}}{a^{1}}\\= a^{ \frac{4}{3} - 1 }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{5} - (\frac{-1}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
5. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{4}{3} - \frac{5}{4} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
6. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
7. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{2}{3} - (\frac{-5}{4}) }= y^{\frac{23}{12}}\\=\sqrt[12]{ y^{23} }=|y|.\sqrt[12]{ y^{11} }\\---------------\)
8. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
9. \(\dfrac{a^{\frac{-4}{3}}}{a^{-1}}\\= a^{ \frac{-4}{3} - (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
10. \(\dfrac{y^{-2}}{y^{\frac{1}{2}}}\\= y^{ -2 - \frac{1}{2} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-1}{6} - (\frac{-4}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)