Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{2}}}{y^{-1}}\\= y^{ \frac{-3}{2} - (-1) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-4}{3} - \frac{1}{6} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{2} - \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{4} - (\frac{-1}{3}) }= y^{\frac{19}{12}}\\=\sqrt[12]{ y^{19} }=|y|.\sqrt[12]{ y^{7} }\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{2}{3} - (\frac{-1}{3}) }= y^{1}\\\\---------------\)
6. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-2}{5} - \frac{3}{4} }= a^{\frac{-23}{20}}\\=\frac{1}{\sqrt[20]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{3} }}=\frac{1}{|a|.\sqrt[20]{ a^{3} }} \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{6} - \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
9. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{3}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
10. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{3}{2}}}\\= x^{ \frac{2}{5} - \frac{3}{2} }= x^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[10]{ x }}=\frac{1}{|x|.\sqrt[10]{ x }} \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x^{2}|}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-1}{6}}}\\= x^{ 1 - (\frac{-1}{6}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
12. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{4}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)