Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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