Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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