Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{6}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{6} - \frac{2}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
4. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{5}{3} - (\frac{-1}{6}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{2} - \frac{1}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
6. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{5}{3} - \frac{5}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
7. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-5}{3} - \frac{1}{5} }= a^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ a^{28} }}\\=\frac{1}{a.\sqrt[15]{ a^{13} }}=\frac{1}{a.\sqrt[15]{ a^{13} }} \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-4}{5} - (\frac{-5}{4}) }= x^{\frac{9}{20}}\\=\sqrt[20]{ x^{9} }\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{-1}{2}}}\\= a^{ -1 - (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{-4}{5}}}\\= x^{ 1 - (\frac{-4}{5}) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
11. \(\dfrac{a^{2}}{a^{\frac{5}{2}}}\\= a^{ 2 - \frac{5}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{5}{2} - \frac{5}{3} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)