Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{4}}}{a^{2}}\\= a^{ \frac{-3}{4} - 2 }= a^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ a^{11} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }}=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{3}|}\\---------------\)
2. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{4}{3} - (\frac{-4}{5}) }= y^{\frac{32}{15}}\\=\sqrt[15]{ y^{32} }=y^{2}.\sqrt[15]{ y^{2} }\\---------------\)
3. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{4}{3}}}\\= a^{ \frac{2}{5} - \frac{4}{3} }= a^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ a^{14} }}=\frac{1}{\sqrt[15]{ a^{14} }}. \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a}\\---------------\)
4. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-5}{2} - (\frac{-4}{3}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{4}{3} - (\frac{-2}{3}) }= a^{2}\\\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{-4}{3}}}\\= q^{ -1 - (\frac{-4}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
7. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-5}{3} - (\frac{-3}{2}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{2} - (\frac{-1}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
9. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{1}{6}}}\\= q^{ \frac{2}{5} - \frac{1}{6} }= q^{\frac{7}{30}}\\=\sqrt[30]{ q^{7} }\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{4}{5}}}\\= y^{ 1 - \frac{4}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
11. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{2}{5} - \frac{1}{2} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
12. \(\dfrac{x^{2}}{x^{\frac{-1}{2}}}\\= x^{ 2 - (\frac{-1}{2}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)