Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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