Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-5}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
2. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-5}{2} - \frac{5}{3} }= q^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ q^{25} }}\\=\frac{1}{|q^{4}|.\sqrt[6]{ q }}=\frac{1}{|q^{4}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{5}|}\\---------------\)
3. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{3}{2}}}\\= a^{ \frac{5}{6} - \frac{3}{2} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
4. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{1}{2} - (\frac{-1}{4}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{2}{3}}}\\= x^{ -1 - \frac{2}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{5} - \frac{1}{3} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
8. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{5}{4} - (\frac{-5}{4}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
9. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-5}{3} - \frac{5}{6} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
10. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{4}{3}}}\\= y^{ \frac{4}{5} - \frac{4}{3} }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
11. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{3}{2} - (\frac{-3}{2}) }= y^{3}\\\\---------------\)
12. \(\dfrac{y^{\frac{1}{4}}}{y^{1}}\\= y^{ \frac{1}{4} - 1 }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)