Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{3} - \frac{2}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{3}{4} - (\frac{-3}{5}) }= q^{\frac{27}{20}}\\=\sqrt[20]{ q^{27} }=|q|.\sqrt[20]{ q^{7} }\\---------------\)
3. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{2} - (\frac{-3}{4}) }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{3}{5} - (\frac{-1}{4}) }= x^{\frac{17}{20}}\\=\sqrt[20]{ x^{17} }\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{1}{4} - \frac{4}{5} }= q^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ q^{11} }}=\frac{1}{\sqrt[20]{ q^{11} }}. \color{purple}{\frac{\sqrt[20]{ q^{9} }}{\sqrt[20]{ q^{9} }}} \\=\frac{\sqrt[20]{ q^{9} }}{|q|}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{-4}{5}}}\\= q^{ -1 - (\frac{-4}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
8. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{4}{3}}}\\= a^{ \frac{5}{6} - \frac{4}{3} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
9. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{3}{4} - (\frac{-1}{3}) }= a^{\frac{13}{12}}\\=\sqrt[12]{ a^{13} }=|a|.\sqrt[12]{ a }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{5}{6}}}\\= x^{ -1 - \frac{5}{6} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{1}{4}}}\\= a^{ \frac{3}{4} - \frac{1}{4} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{6}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)