Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{2}}}{q^{1}}\\= q^{ \frac{-3}{2} - 1 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{2}{3} - \frac{1}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
3. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-2}{3} - \frac{2}{5} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{6} - \frac{1}{4} }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
5. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-2}{5} - \frac{1}{6} }= y^{\frac{-17}{30}}\\=\frac{1}{\sqrt[30]{ y^{17} }}=\frac{1}{\sqrt[30]{ y^{17} }}. \color{purple}{\frac{\sqrt[30]{ y^{13} }}{\sqrt[30]{ y^{13} }}} \\=\frac{\sqrt[30]{ y^{13} }}{|y|}\\---------------\)
6. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{4}{5} - (\frac{-5}{6}) }= a^{\frac{49}{30}}\\=\sqrt[30]{ a^{49} }=|a|.\sqrt[30]{ a^{19} }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{2}{3}}}\\= x^{ -1 - \frac{2}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-4}{5} - \frac{5}{2} }= a^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ a^{33} }}\\=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{4}|}\\---------------\)
9. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{3}{4} - (\frac{-4}{3}) }= x^{\frac{25}{12}}\\=\sqrt[12]{ x^{25} }=|x^{2}|.\sqrt[12]{ x }\\---------------\)
10. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-2}{3} - \frac{2}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{5} - (\frac{-1}{6}) }= q^{\frac{11}{30}}\\=\sqrt[30]{ q^{11} }\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{-1}{2}}}\\= x^{ -1 - (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)