Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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