Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{2}{3} - \frac{3}{4} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-1}{2} - (\frac{-3}{5}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{1}{2}}}\\= a^{ -1 - \frac{1}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{3}{5} - \frac{1}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
5. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{1}{4} - (\frac{-4}{3}) }= a^{\frac{19}{12}}\\=\sqrt[12]{ a^{19} }=|a|.\sqrt[12]{ a^{7} }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{6} - (\frac{-3}{4}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{-5}{3}}}\\= x^{ -1 - (\frac{-5}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
8. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{1}{4}}}\\= q^{ \frac{3}{4} - \frac{1}{4} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\dfrac{a^{\frac{-3}{4}}}{a^{-2}}\\= a^{ \frac{-3}{4} - (-2) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{2}) }= q^{0}\\=1\\---------------\)
11. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{6} - (\frac{-1}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{2} - \frac{1}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)