Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{-1}{6}}}\\= x^{ 1 - (\frac{-1}{6}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-4}{3} - \frac{3}{5} }= a^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ a^{29} }}\\=\frac{1}{a.\sqrt[15]{ a^{14} }}=\frac{1}{a.\sqrt[15]{ a^{14} }} \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{5}{6} - (\frac{-2}{3}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
4. \(\dfrac{a^{\frac{-2}{3}}}{a^{1}}\\= a^{ \frac{-2}{3} - 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{5}{3} - \frac{4}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{q^{\frac{1}{5}}}{q^{1}}\\= q^{ \frac{1}{5} - 1 }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
7. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-3}{5} - \frac{2}{3} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{3}{5} - \frac{2}{3} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{2}{5}}}\\= a^{ -1 - \frac{2}{5} }= a^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ a^{7} }}\\=\frac{1}{a.\sqrt[5]{ a^{2} }}=\frac{1}{a.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{4}{3} - \frac{1}{2} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{1}{2} - \frac{3}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{6}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)