Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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