Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{5}}}{y^{-1}}\\= y^{ \frac{-3}{5} - (-1) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
3. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-5}{2} - \frac{5}{3} }= x^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ x^{25} }}\\=\frac{1}{|x^{4}|.\sqrt[6]{ x }}=\frac{1}{|x^{4}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{5}|}\\---------------\)
4. \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\\= q^{ \frac{5}{4} - 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{2} - (\frac{-1}{2}) }= q^{1}\\\\---------------\)
6. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{6} - \frac{2}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{4} - \frac{5}{6} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{3} - \frac{3}{5} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{6}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\\= a^{ 1 - (\frac{-5}{2}) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
11. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-4}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{5} - \frac{1}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)