Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-1}{6} - (\frac{-2}{3}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(\dfrac{a^{\frac{4}{3}}}{a^{-1}}\\= a^{ \frac{4}{3} - (-1) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{2}{5}}}\\= q^{ -1 - \frac{2}{5} }= q^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ q^{7} }}\\=\frac{1}{q.\sqrt[5]{ q^{2} }}=\frac{1}{q.\sqrt[5]{ q^{2} }} \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-3}{4} - \frac{3}{4} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{1}{3} - \frac{3}{5} }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
6. \(\dfrac{y^{\frac{-2}{3}}}{y^{-1}}\\= y^{ \frac{-2}{3} - (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
7. \(\dfrac{a^{\frac{-3}{2}}}{a^{1}}\\= a^{ \frac{-3}{2} - 1 }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
8. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{1}{5}}}\\= x^{ \frac{4}{5} - \frac{1}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{3}) }= a^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-3}{4} - \frac{2}{5} }= x^{\frac{-23}{20}}\\=\frac{1}{\sqrt[20]{ x^{23} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{3} }}=\frac{1}{|x|.\sqrt[20]{ x^{3} }} \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{-5}{6}}}\\= a^{ 1 - (\frac{-5}{6}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)