Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{2} - (\frac{-1}{2}) }= x^{1}\\\\---------------\)
2. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{3}{5} - (\frac{-5}{4}) }= y^{\frac{37}{20}}\\=\sqrt[20]{ y^{37} }=|y|.\sqrt[20]{ y^{17} }\\---------------\)
3. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{2}{5} - (\frac{-1}{3}) }= x^{\frac{11}{15}}\\=\sqrt[15]{ x^{11} }\\---------------\)
4. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{5}{4} - \frac{2}{3} }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
5. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{6} - \frac{2}{3} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{1}{2} - \frac{4}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{2}}\\= x^{ \frac{2}{3} - 2 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-3}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
9. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{5}{3} - \frac{1}{3} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{a^{-1}}{a^{\frac{-5}{4}}}\\= a^{ -1 - (\frac{-5}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
11. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-5}{3}) }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{3} - \frac{5}{6} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)