Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{1}{3} - (\frac{-3}{2}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{1}{5}}}\\= a^{ 1 - \frac{1}{5} }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
3. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{4}{3} - (\frac{-3}{5}) }= a^{\frac{29}{15}}\\=\sqrt[15]{ a^{29} }=a.\sqrt[15]{ a^{14} }\\---------------\)
4. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-3}{2} - (\frac{-4}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{4}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
6. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{3}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{2} - (\frac{-2}{3}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{y^{\frac{-5}{6}}}{y^{-1}}\\= y^{ \frac{-5}{6} - (-1) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{6} - \frac{3}{2} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{2}}\\= q^{ \frac{-1}{2} - 2 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-1}{4} - (\frac{-3}{4}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{-4}{3}}}\\= y^{ -1 - (\frac{-4}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)