Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{4} - (\frac{-1}{5}) }= x^{\frac{9}{20}}\\=\sqrt[20]{ x^{9} }\\---------------\)
2. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
3. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{3}{2} - \frac{1}{2} }= a^{1}\\\\---------------\)
4. \(\dfrac{q^{\frac{-5}{2}}}{q^{1}}\\= q^{ \frac{-5}{2} - 1 }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
5. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{3}{4} - (\frac{-2}{5}) }= x^{\frac{23}{20}}\\=\sqrt[20]{ x^{23} }=|x|.\sqrt[20]{ x^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-4}{5} - (\frac{-5}{4}) }= x^{\frac{9}{20}}\\=\sqrt[20]{ x^{9} }\\---------------\)
7. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{5}{6}}}\\= q^{ \frac{2}{5} - \frac{5}{6} }= q^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ q^{13} }}=\frac{1}{\sqrt[30]{ q^{13} }}. \color{purple}{\frac{\sqrt[30]{ q^{17} }}{\sqrt[30]{ q^{17} }}} \\=\frac{\sqrt[30]{ q^{17} }}{|q|}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{5} - (\frac{-5}{6}) }= a^{\frac{19}{30}}\\=\sqrt[30]{ a^{19} }\\---------------\)
9. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{3} - \frac{2}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
10. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{6} - \frac{1}{2} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-1}{4} - \frac{5}{3} }= y^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ y^{23} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{11} }}=\frac{1}{|y|.\sqrt[12]{ y^{11} }} \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{6} - \frac{1}{3} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)