Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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