Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{1}{6}}}\\= x^{ \frac{5}{3} - \frac{1}{6} }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
2. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{5} - (\frac{-1}{3}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{2}{5} - \frac{5}{3} }= q^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ q^{19} }}\\=\frac{1}{q.\sqrt[15]{ q^{4} }}=\frac{1}{q.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-5}{2} - (\frac{-1}{3}) }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
5. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-3}{4} - \frac{3}{4} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
6. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
7. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-2}{3} - \frac{2}{5} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-3}{5} - \frac{2}{5} }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\dfrac{q^{\frac{2}{5}}}{q^{1}}\\= q^{ \frac{2}{5} - 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
10. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-3}{5} - (\frac{-1}{2}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
11. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{6} - \frac{2}{5} }= x^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ x^{7} }}=\frac{1}{\sqrt[30]{ x^{7} }}. \color{purple}{\frac{\sqrt[30]{ x^{23} }}{\sqrt[30]{ x^{23} }}} \\=\frac{\sqrt[30]{ x^{23} }}{|x|}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)