Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-4}{3} - \frac{1}{2} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{-5}{2}}}{q^{1}}\\= q^{ \frac{-5}{2} - 1 }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
3. \(\dfrac{a^{\frac{1}{4}}}{a^{2}}\\= a^{ \frac{1}{4} - 2 }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{1}{5} - (\frac{-5}{6}) }= a^{\frac{31}{30}}\\=\sqrt[30]{ a^{31} }=|a|.\sqrt[30]{ a }\\---------------\)
5. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{2}{5} - \frac{5}{3} }= y^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ y^{19} }}\\=\frac{1}{y.\sqrt[15]{ y^{4} }}=\frac{1}{y.\sqrt[15]{ y^{4} }} \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-1}{3} - \frac{1}{5} }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
7. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{1}{3} - \frac{1}{3} }= y^{0}\\=1\\---------------\)
8. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{5}{4}}}\\= y^{ \frac{1}{6} - \frac{5}{4} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{5}{6}}}\\= q^{ -1 - \frac{5}{6} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{2} - \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
12. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{4} - \frac{5}{4} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)