Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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