Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-2}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
2. \(\dfrac{x^{1}}{x^{\frac{2}{5}}}\\= x^{ 1 - \frac{2}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{-4}{5}}}\\= a^{ 1 - (\frac{-4}{5}) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
4. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-2}{5} - \frac{2}{5} }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
5. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{5}{3}}}\\= x^{ \frac{1}{6} - \frac{5}{3} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-5}{2} - (\frac{-4}{3}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-2}{3} - \frac{5}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
8. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{3} - \frac{3}{2} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{2} - \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{6} - \frac{1}{2} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{1}{2} - (\frac{-1}{5}) }= a^{\frac{7}{10}}\\=\sqrt[10]{ a^{7} }\\---------------\)
12. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{4}{5} - (\frac{-5}{3}) }= a^{\frac{37}{15}}\\=\sqrt[15]{ a^{37} }=a^{2}.\sqrt[15]{ a^{7} }\\---------------\)