Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{1}{2} - \frac{5}{3} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-5}{6} - \frac{4}{5} }= a^{\frac{-49}{30}}\\=\frac{1}{\sqrt[30]{ a^{49} }}\\=\frac{1}{|a|.\sqrt[30]{ a^{19} }}=\frac{1}{|a|.\sqrt[30]{ a^{19} }} \color{purple}{\frac{\sqrt[30]{ a^{11} }}{\sqrt[30]{ a^{11} }}} \\=\frac{\sqrt[30]{ a^{11} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-1}{3} - \frac{3}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{4} - \frac{2}{3} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
5. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{1}{5} - \frac{1}{6} }= y^{\frac{1}{30}}\\=\sqrt[30]{ y }\\---------------\)
6. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{3}{4} - (\frac{-2}{5}) }= q^{\frac{23}{20}}\\=\sqrt[20]{ q^{23} }=|q|.\sqrt[20]{ q^{3} }\\---------------\)
7. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{5}{2} - (\frac{-2}{5}) }= x^{\frac{29}{10}}\\=\sqrt[10]{ x^{29} }=|x^{2}|.\sqrt[10]{ x^{9} }\\---------------\)
8. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{4}{5} - \frac{5}{2} }= q^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{7} }}=\frac{1}{|q|.\sqrt[10]{ q^{7} }} \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{6}}}\\= q^{ \frac{2}{3} - \frac{1}{6} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{4}{3} - (\frac{-1}{2}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
12. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-5}{6} - \frac{3}{4} }= a^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{7} }}=\frac{1}{|a|.\sqrt[12]{ a^{7} }} \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a^{2}|}\\---------------\)