Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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