Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{5} - (\frac{-1}{2}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{1}}\\= y^{ \frac{2}{3} - 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{2} - (\frac{-1}{2}) }= a^{1}\\\\---------------\)
4. \(\dfrac{x^{2}}{x^{\frac{2}{3}}}\\= x^{ 2 - \frac{2}{3} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{1}{6}}}\\= y^{ -1 - \frac{1}{6} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{4}{5}}}{a^{-2}}\\= a^{ \frac{4}{5} - (-2) }= a^{\frac{14}{5}}\\=\sqrt[5]{ a^{14} }=a^{2}.\sqrt[5]{ a^{4} }\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{1}{2} - \frac{4}{5} }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
9. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{4}{5} - (\frac{-5}{4}) }= y^{\frac{41}{20}}\\=\sqrt[20]{ y^{41} }=|y^{2}|.\sqrt[20]{ y }\\---------------\)
10. \(\dfrac{q^{-2}}{q^{\frac{1}{2}}}\\= q^{ -2 - \frac{1}{2} }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
11. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{2}{3} - (\frac{-2}{5}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
12. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{5}{3} - (\frac{-5}{4}) }= y^{\frac{35}{12}}\\=\sqrt[12]{ y^{35} }=|y^{2}|.\sqrt[12]{ y^{11} }\\---------------\)