Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{2} - (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
3. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{3} - \frac{2}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
4. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{1}{5} - \frac{5}{4} }= x^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ x^{21} }}\\=\frac{1}{|x|.\sqrt[20]{ x }}=\frac{1}{|x|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{3}{4}}}\\= x^{ \frac{3}{4} - \frac{3}{4} }= x^{0}\\=1\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{1}{6}}}\\= q^{ -1 - \frac{1}{6} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{4}{3}}}\\= x^{ -1 - \frac{4}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
9. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{4} - (\frac{-2}{3}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
10. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
11. \(\dfrac{q^{2}}{q^{\frac{5}{4}}}\\= q^{ 2 - \frac{5}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
12. \(\dfrac{a^{\frac{1}{4}}}{a^{-1}}\\= a^{ \frac{1}{4} - (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)