Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-5}{4} - (\frac{-1}{4}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
2. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{6} - \frac{3}{5} }= y^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ y^{13} }}=\frac{1}{\sqrt[30]{ y^{13} }}. \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y|}\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{1}{5}}}\\= a^{ -1 - \frac{1}{5} }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
4. \(\dfrac{q^{1}}{q^{-2}}\\= q^{ 1 - (-2) }= q^{3}\\\\---------------\)
5. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{5}{3} - \frac{3}{4} }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
6. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{4}{3} - (\frac{-1}{4}) }= y^{\frac{19}{12}}\\=\sqrt[12]{ y^{19} }=|y|.\sqrt[12]{ y^{7} }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{-4}{3}}}\\= x^{ -1 - (\frac{-4}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-2}{3} - \frac{5}{6} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{-3}{5}}}\\= x^{ -1 - (\frac{-3}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{3} - (\frac{-1}{2}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-1}{6} - (\frac{-4}{5}) }= a^{\frac{19}{30}}\\=\sqrt[30]{ a^{19} }\\---------------\)
12. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{3}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)