Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{5}{4} - \frac{1}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{2} - (\frac{-1}{2}) }= y^{1}\\\\---------------\)
3. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{3}{2} - (\frac{-2}{5}) }= a^{\frac{19}{10}}\\=\sqrt[10]{ a^{19} }=|a|.\sqrt[10]{ a^{9} }\\---------------\)
4. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{5}{2}}}\\= x^{ \frac{2}{5} - \frac{5}{2} }= x^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ x^{21} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x }}=\frac{1}{|x^{2}|.\sqrt[10]{ x }} \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x^{3}|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{3} - (\frac{-4}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{6}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
7. \(\dfrac{q^{-2}}{q^{\frac{-4}{3}}}\\= q^{ -2 - (\frac{-4}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{6} - (\frac{-2}{5}) }= x^{\frac{7}{30}}\\=\sqrt[30]{ x^{7} }\\---------------\)
9. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{3}{2}}}\\= y^{ \frac{4}{3} - \frac{3}{2} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(\dfrac{q^{\frac{-3}{2}}}{q^{2}}\\= q^{ \frac{-3}{2} - 2 }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
11. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-3}{2} - \frac{1}{4} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-5}{3} - \frac{2}{5} }= x^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ x^{31} }}\\=\frac{1}{x^{2}.\sqrt[15]{ x }}=\frac{1}{x^{2}.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{3}}\\---------------\)