Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{3}}}{a^{-1}}\\= a^{ \frac{2}{3} - (-1) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-2}{3} - \frac{5}{2} }= y^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ y^{19} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y }}=\frac{1}{|y^{3}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{4}|}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{2}{5} - \frac{3}{2} }= y^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[10]{ y }}=\frac{1}{|y|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{q^{-1}}{q^{\frac{-3}{4}}}\\= q^{ -1 - (\frac{-3}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{6} - (\frac{-3}{4}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
7. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{2}{3} - \frac{3}{4} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
8. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{1}{3} - (\frac{-3}{4}) }= y^{\frac{13}{12}}\\=\sqrt[12]{ y^{13} }=|y|.\sqrt[12]{ y }\\---------------\)
9. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-3}{4} - \frac{3}{5} }= y^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ y^{27} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{7} }}=\frac{1}{|y|.\sqrt[20]{ y^{7} }} \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-2}{3} - \frac{3}{5} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{5}{3}}}\\= y^{ -1 - \frac{5}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
12. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{1}{6} - (\frac{-3}{5}) }= a^{\frac{23}{30}}\\=\sqrt[30]{ a^{23} }\\---------------\)