Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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