Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{2}{3} - (\frac{-1}{3}) }= q^{1}\\\\---------------\)
2. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-3}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
4. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{2}{5} - (\frac{-5}{6}) }= y^{\frac{37}{30}}\\=\sqrt[30]{ y^{37} }=|y|.\sqrt[30]{ y^{7} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{6}}}{a^{1}}\\= a^{ \frac{-1}{6} - 1 }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{5}{3}}}{y^{2}}\\= y^{ \frac{5}{3} - 2 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{-5}{3}}}\\= q^{ -1 - (\frac{-5}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-1}{4} - (\frac{-5}{6}) }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{-5}{2}}}\\= a^{ -1 - (\frac{-5}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
10. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{4} - (\frac{-1}{3}) }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{2} - (\frac{-1}{6}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{1}{3}}}\\= q^{ 1 - \frac{1}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)