Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-2}}{a^{\frac{-2}{3}}}\\= a^{ -2 - (\frac{-2}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
2. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-5}{4} - \frac{4}{5} }= y^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ y^{41} }}\\=\frac{1}{|y^{2}|.\sqrt[20]{ y }}=\frac{1}{|y^{2}|.\sqrt[20]{ y }} \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{5}}}{x^{-2}}\\= x^{ \frac{-1}{5} - (-2) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{6} - \frac{1}{3} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
5. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{1}{2} - \frac{3}{5} }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{4} - (\frac{-3}{4}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{1}}\\= q^{ \frac{2}{3} - 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
8. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{4}{5} - \frac{5}{2} }= q^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{7} }}=\frac{1}{|q|.\sqrt[10]{ q^{7} }} \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{5} - (\frac{-1}{2}) }= x^{\frac{7}{10}}\\=\sqrt[10]{ x^{7} }\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{5}{3}}}\\= y^{ 1 - \frac{5}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
11. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-5}{6} - (\frac{-1}{5}) }= y^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ y^{19} }}=\frac{1}{\sqrt[30]{ y^{19} }}. \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y|}\\---------------\)
12. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{6} - (\frac{-4}{3}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)