Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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