Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{6} - \frac{1}{2} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
2. \(\dfrac{x^{\frac{-4}{5}}}{x^{1}}\\= x^{ \frac{-4}{5} - 1 }= x^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ x^{9} }}\\=\frac{1}{x.\sqrt[5]{ x^{4} }}=\frac{1}{x.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{3} - \frac{1}{4} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
4. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{5}{2}}}\\= x^{ \frac{1}{6} - \frac{5}{2} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
5. \(\dfrac{a^{1}}{a^{\frac{2}{3}}}\\= a^{ 1 - \frac{2}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{5} - \frac{1}{2} }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)
7. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-1}{6} - (\frac{-3}{4}) }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{1}}\\= a^{ \frac{1}{2} - 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
9. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-2}{3} - \frac{1}{2} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{3} - \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-5}{2} - \frac{2}{3} }= x^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ x^{19} }}\\=\frac{1}{|x^{3}|.\sqrt[6]{ x }}=\frac{1}{|x^{3}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{4}|}\\---------------\)