Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{5}{4} - (\frac{-5}{6}) }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
2. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{6} - (\frac{-1}{3}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
3. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{3}{5}}}\\= a^{ -1 - \frac{3}{5} }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{2} - \frac{2}{3} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
6. \(\dfrac{a^{\frac{5}{6}}}{a^{-1}}\\= a^{ \frac{5}{6} - (-1) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{2}{3} - (\frac{-1}{6}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
8. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{2}{3} - \frac{2}{3} }= x^{0}\\=1\\---------------\)
9. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-5}{3} - (\frac{-2}{3}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
10. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-4}{3} - (\frac{-5}{2}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-1}{2} - \frac{5}{6} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{6} - \frac{1}{3} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)