Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{-1}}\\= q^{ 1 - (-1) }= q^{2}\\\\---------------\)
2. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{1}{6}}}\\= x^{ \frac{1}{5} - \frac{1}{6} }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-5}{6} - \frac{2}{3} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-4}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
6. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{3}{5}}}\\= q^{ \frac{-2}{3} - \frac{3}{5} }= q^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ q^{19} }}\\=\frac{1}{q.\sqrt[15]{ q^{4} }}=\frac{1}{q.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
8. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-5}{2} - \frac{5}{3} }= x^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ x^{25} }}\\=\frac{1}{|x^{4}|.\sqrt[6]{ x }}=\frac{1}{|x^{4}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{5}|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{-1}}\\= a^{ \frac{-1}{2} - (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\dfrac{x^{\frac{2}{5}}}{x^{2}}\\= x^{ \frac{2}{5} - 2 }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-3}{2} - (\frac{-1}{5}) }= q^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{3} }}=\frac{1}{|q|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-2}{5} - \frac{2}{5} }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)