Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{2}}}{x^{-1}}\\= x^{ \frac{-5}{2} - (-1) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{4} - \frac{1}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{-5}{4}}}\\= y^{ -1 - (\frac{-5}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-5}{6} - \frac{4}{5} }= x^{\frac{-49}{30}}\\=\frac{1}{\sqrt[30]{ x^{49} }}\\=\frac{1}{|x|.\sqrt[30]{ x^{19} }}=\frac{1}{|x|.\sqrt[30]{ x^{19} }} \color{purple}{\frac{\sqrt[30]{ x^{11} }}{\sqrt[30]{ x^{11} }}} \\=\frac{\sqrt[30]{ x^{11} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{1}{3} - \frac{3}{5} }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
6. \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
7. \(\dfrac{q^{2}}{q^{1}}\\= q^{ 2 - 1 }= q^{1}\\\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-5}{4}}}\\= y^{ 1 - (\frac{-5}{4}) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
9. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{2}{5} - (\frac{-1}{2}) }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
10. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{5}{4} - (\frac{-1}{3}) }= x^{\frac{19}{12}}\\=\sqrt[12]{ x^{19} }=|x|.\sqrt[12]{ x^{7} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-1}{6} - \frac{4}{5} }= y^{\frac{-29}{30}}\\=\frac{1}{\sqrt[30]{ y^{29} }}=\frac{1}{\sqrt[30]{ y^{29} }}. \color{purple}{\frac{\sqrt[30]{ y }}{\sqrt[30]{ y }}} \\=\frac{\sqrt[30]{ y }}{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{2}{3} - (\frac{-1}{5}) }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)