Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-4}{5}}}{a^{2}}\\= a^{ \frac{-4}{5} - 2 }= a^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ a^{14} }}\\=\frac{1}{a^{2}.\sqrt[5]{ a^{4} }}=\frac{1}{a^{2}.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{3}}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{2}}\\= a^{ \frac{-1}{2} - 2 }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
4. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{2} - \frac{5}{3} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{4} - \frac{2}{3} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-2}{5}}}\\= x^{ 1 - (\frac{-2}{5}) }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{2}{3}}}\\= a^{ \frac{5}{6} - \frac{2}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{q^{\frac{-5}{4}}}{q^{1}}\\= q^{ \frac{-5}{4} - 1 }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{4}{3}}}\\= q^{ -1 - \frac{4}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
10. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{3}{5}}}\\= q^{ \frac{3}{5} - \frac{3}{5} }= q^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-3}{5} - \frac{2}{3} }= x^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ x^{19} }}\\=\frac{1}{x.\sqrt[15]{ x^{4} }}=\frac{1}{x.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-1}{2} - \frac{3}{2} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)