Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-2}{3} - \frac{1}{6} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
3. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{4}{5} - (\frac{-4}{3}) }= a^{\frac{32}{15}}\\=\sqrt[15]{ a^{32} }=a^{2}.\sqrt[15]{ a^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{5}{3} - (\frac{-1}{5}) }= y^{\frac{28}{15}}\\=\sqrt[15]{ y^{28} }=y.\sqrt[15]{ y^{13} }\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{2} - \frac{1}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
6. \(\dfrac{q^{1}}{q^{-1}}\\= q^{ 1 - (-1) }= q^{2}\\\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-1}{4} - \frac{4}{3} }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{4}{3} - \frac{1}{2} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{y^{-2}}{y^{\frac{3}{2}}}\\= y^{ -2 - \frac{3}{2} }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{3} - (\frac{-1}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{4}{3} - (\frac{-4}{5}) }= q^{\frac{32}{15}}\\=\sqrt[15]{ q^{32} }=q^{2}.\sqrt[15]{ q^{2} }\\---------------\)