Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{5}}}{a^{-1}}\\= a^{ \frac{1}{5} - (-1) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
2. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{5} - (\frac{-1}{6}) }= q^{\frac{11}{30}}\\=\sqrt[30]{ q^{11} }\\---------------\)
3. \(\dfrac{q^{\frac{-2}{5}}}{q^{1}}\\= q^{ \frac{-2}{5} - 1 }= q^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ q^{7} }}\\=\frac{1}{q.\sqrt[5]{ q^{2} }}=\frac{1}{q.\sqrt[5]{ q^{2} }} \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{2}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
5. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{2}{3} - (\frac{-2}{5}) }= a^{\frac{16}{15}}\\=\sqrt[15]{ a^{16} }=a.\sqrt[15]{ a }\\---------------\)
6. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{2}{5} - \frac{4}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
7. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-2}{3} - \frac{2}{5} }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{6} - \frac{5}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{2}{3} - \frac{5}{6} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{4}}}{q^{-1}}\\= q^{ \frac{-1}{4} - (-1) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{5}}}{x^{1}}\\= x^{ \frac{-1}{5} - 1 }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-4}{5} - \frac{2}{3} }= x^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ x^{22} }}\\=\frac{1}{x.\sqrt[15]{ x^{7} }}=\frac{1}{x.\sqrt[15]{ x^{7} }} \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x^{2}}\\---------------\)