Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{3} - \frac{1}{4} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
2. \(\dfrac{a^{-2}}{a^{\frac{-1}{5}}}\\= a^{ -2 - (\frac{-1}{5}) }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-3}{2}}}{q^{1}}\\= q^{ \frac{-3}{2} - 1 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{1}{4} - (\frac{-5}{4}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{3}{2} - \frac{4}{5} }= y^{\frac{7}{10}}\\=\sqrt[10]{ y^{7} }\\---------------\)
6. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{1}{4} - (\frac{-1}{5}) }= y^{\frac{9}{20}}\\=\sqrt[20]{ y^{9} }\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{1}{4}}}\\= q^{ -1 - \frac{1}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{4}{3} - \frac{4}{3} }= q^{0}\\=1\\---------------\)
9. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{5} - \frac{1}{2} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-1}{4} - (\frac{-2}{3}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
11. \(\dfrac{a^{-1}}{a^{\frac{-2}{3}}}\\= a^{ -1 - (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
12. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{5}{4} - \frac{2}{3} }= a^{\frac{7}{12}}\\=\sqrt[12]{ a^{7} }\\---------------\)