Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
2. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{4}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
3. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{4}{5}}}\\= y^{ \frac{5}{6} - \frac{4}{5} }= y^{\frac{1}{30}}\\=\sqrt[30]{ y }\\---------------\)
4. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-3}{5} - \frac{1}{2} }= q^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[10]{ q }}=\frac{1}{|q|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{5}{3} - \frac{2}{3} }= a^{1}\\\\---------------\)
6. \(\dfrac{y^{\frac{-3}{2}}}{y^{1}}\\= y^{ \frac{-3}{2} - 1 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{1}{3}}}\\= a^{ -1 - \frac{1}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{2}}\\= q^{ -1 - 2 }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
9. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{5}{6} - (\frac{-1}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-1}{2} - \frac{5}{2} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
11. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-5}{6} - (\frac{-3}{5}) }= x^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ x^{7} }}=\frac{1}{\sqrt[30]{ x^{7} }}. \color{purple}{\frac{\sqrt[30]{ x^{23} }}{\sqrt[30]{ x^{23} }}} \\=\frac{\sqrt[30]{ x^{23} }}{|x|}\\---------------\)
12. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)