Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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