Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{2}}\\= a^{ -1 - 2 }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
2. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{6} - \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{1}{4}}}\\= q^{ -1 - \frac{1}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-1}{5} - (\frac{-4}{5}) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
5. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{3}{4} - (\frac{-4}{5}) }= q^{\frac{31}{20}}\\=\sqrt[20]{ q^{31} }=|q|.\sqrt[20]{ q^{11} }\\---------------\)
6. \(\dfrac{a^{\frac{-1}{6}}}{a^{-2}}\\= a^{ \frac{-1}{6} - (-2) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
7. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-5}{6} - \frac{2}{5} }= q^{\frac{-37}{30}}\\=\frac{1}{\sqrt[30]{ q^{37} }}\\=\frac{1}{|q|.\sqrt[30]{ q^{7} }}=\frac{1}{|q|.\sqrt[30]{ q^{7} }} \color{purple}{\frac{\sqrt[30]{ q^{23} }}{\sqrt[30]{ q^{23} }}} \\=\frac{\sqrt[30]{ q^{23} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{3} - \frac{4}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{-1}{4}}}\\= y^{ 1 - (\frac{-1}{4}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
11. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{2} - \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)