Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{2}{5} - (\frac{-5}{6}) }= a^{\frac{37}{30}}\\=\sqrt[30]{ a^{37} }=|a|.\sqrt[30]{ a^{7} }\\---------------\)
2. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{4}{3}}}\\= x^{ \frac{5}{4} - \frac{4}{3} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
3. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{2} - (\frac{-2}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{4}{3}}}\\= a^{ -1 - \frac{4}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
5. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{2}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
6. \(\dfrac{x^{1}}{x^{-1}}\\= x^{ 1 - (-1) }= x^{2}\\\\---------------\)
7. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-5}{6} - \frac{2}{5} }= x^{\frac{-37}{30}}\\=\frac{1}{\sqrt[30]{ x^{37} }}\\=\frac{1}{|x|.\sqrt[30]{ x^{7} }}=\frac{1}{|x|.\sqrt[30]{ x^{7} }} \color{purple}{\frac{\sqrt[30]{ x^{23} }}{\sqrt[30]{ x^{23} }}} \\=\frac{\sqrt[30]{ x^{23} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{1}{6}}}\\= x^{ \frac{3}{2} - \frac{1}{6} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
9. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{1}{3} - \frac{5}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{2}) }= x^{2}\\\\---------------\)
11. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{5}{6} - (\frac{-2}{3}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
12. \(\dfrac{a^{\frac{4}{3}}}{a^{-1}}\\= a^{ \frac{4}{3} - (-1) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)