Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-1}{3} - \frac{1}{5} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
2. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{6}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{-4}{5}}}\\= a^{ -1 - (\frac{-4}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{2}{3} - \frac{5}{2} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
5. \(\dfrac{y^{2}}{y^{\frac{3}{4}}}\\= y^{ 2 - \frac{3}{4} }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
6. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-3}{4} - (\frac{-5}{6}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{4} - \frac{5}{6} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
8. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
9. \(\dfrac{x^{\frac{3}{2}}}{x^{-1}}\\= x^{ \frac{3}{2} - (-1) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
10. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{3}{2}}}\\= y^{ \frac{2}{3} - \frac{3}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{1}{3} - \frac{5}{2} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)