Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{2}{3} - \frac{4}{5} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
2. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-2}{5} - \frac{3}{4} }= a^{\frac{-23}{20}}\\=\frac{1}{\sqrt[20]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{3} }}=\frac{1}{|a|.\sqrt[20]{ a^{3} }} \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-2}{3} - \frac{5}{6} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-1}{2} - \frac{5}{2} }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{-2}}\\= q^{ \frac{1}{2} - (-2) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
6. \(\dfrac{y^{\frac{4}{5}}}{y^{-1}}\\= y^{ \frac{4}{5} - (-1) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)
7. \(\dfrac{y^{\frac{5}{6}}}{y^{1}}\\= y^{ \frac{5}{6} - 1 }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{2} - (\frac{-1}{2}) }= a^{1}\\\\---------------\)
9. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-5}{6} - (\frac{-3}{2}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
10. \(\dfrac{x^{-2}}{x^{\frac{-5}{2}}}\\= x^{ -2 - (\frac{-5}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-3}{2} - \frac{4}{5} }= y^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ y^{23} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y^{3} }}=\frac{1}{|y^{2}|.\sqrt[10]{ y^{3} }} \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y^{3}|}\\---------------\)