Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{6}}}{q^{1}}\\= q^{ \frac{1}{6} - 1 }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-1}{2} - \frac{3}{5} }= a^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[10]{ a }}=\frac{1}{|a|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{5}{6}}}\\= y^{ -1 - \frac{5}{6} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{3}{2} - (\frac{-3}{5}) }= x^{\frac{21}{10}}\\=\sqrt[10]{ x^{21} }=|x^{2}|.\sqrt[10]{ x }\\---------------\)
5. \(\dfrac{a^{\frac{3}{2}}}{a^{2}}\\= a^{ \frac{3}{2} - 2 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{2}{5}}}\\= a^{ 1 - \frac{2}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{3} - \frac{1}{4} }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{2}) }= q^{0}\\=1\\---------------\)
9. \(\dfrac{x^{\frac{5}{6}}}{x^{1}}\\= x^{ \frac{5}{6} - 1 }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
10. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{2} - (\frac{-3}{4}) }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{5}{6} - (\frac{-1}{6}) }= a^{1}\\\\---------------\)
12. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{2}) }= x^{2}\\\\---------------\)