Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{2}{5}}}\\= a^{ \frac{5}{6} - \frac{2}{5} }= a^{\frac{13}{30}}\\=\sqrt[30]{ a^{13} }\\---------------\)
2. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{2}{5} - (\frac{-4}{5}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{3}{4}}}\\= a^{ -1 - \frac{3}{4} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-2}{3} - \frac{4}{3} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-2}{3} - \frac{1}{4} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
6. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-3}{4} - (\frac{-1}{4}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{2}}}{x^{-2}}\\= x^{ \frac{-1}{2} - (-2) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-1}{2} - \frac{3}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-5}{4}}}{q^{-2}}\\= q^{ \frac{-5}{4} - (-2) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
10. \(\dfrac{q^{2}}{q^{\frac{-5}{4}}}\\= q^{ 2 - (\frac{-5}{4}) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)
11. \(\dfrac{a^{-1}}{a^{\frac{-4}{5}}}\\= a^{ -1 - (\frac{-4}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
12. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{3} - \frac{1}{4} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)