Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{5}{4} - (\frac{-2}{3}) }= x^{\frac{23}{12}}\\=\sqrt[12]{ x^{23} }=|x|.\sqrt[12]{ x^{11} }\\---------------\)
2. \(\dfrac{q^{\frac{-3}{2}}}{q^{-1}}\\= q^{ \frac{-3}{2} - (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\dfrac{q^{\frac{-3}{5}}}{q^{-1}}\\= q^{ \frac{-3}{5} - (-1) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{1}{6}}}\\= x^{ -1 - \frac{1}{6} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-3}{5} - \frac{2}{3} }= q^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ q^{19} }}\\=\frac{1}{q.\sqrt[15]{ q^{4} }}=\frac{1}{q.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{5}{3}}}{x^{-1}}\\= x^{ \frac{5}{3} - (-1) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-2}{3} - \frac{5}{6} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{2}}\\= y^{ \frac{-2}{3} - 2 }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-1}{2} - \frac{2}{5} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
10. \(\dfrac{q^{2}}{q^{\frac{5}{3}}}\\= q^{ 2 - \frac{5}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{4} - (\frac{-1}{3}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
12. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{1}{4} - \frac{3}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)