Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{4} - \frac{5}{2} }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{6} - (\frac{-1}{3}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\dfrac{x^{\frac{-5}{2}}}{x^{1}}\\= x^{ \frac{-5}{2} - 1 }= x^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ x^{7} } }\\=\frac{1}{|x^{3}|. \sqrt{ x } }=\frac{1}{|x^{3}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{4}|}\\---------------\)
4. \(\dfrac{y^{-1}}{y^{\frac{2}{3}}}\\= y^{ -1 - \frac{2}{3} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-5}{4} - (\frac{-5}{3}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{-1}}\\= x^{ \frac{-1}{3} - (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{4} - (\frac{-1}{2}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
8. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-4}{3} - \frac{3}{4} }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{5}{4}}}\\= y^{ 1 - \frac{5}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{-4}{3}}}\\= a^{ 1 - (\frac{-4}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-3}{4} - (\frac{-3}{2}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{5}{6}}}\\= y^{ -1 - \frac{5}{6} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)