Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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