Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{1}{3}}}\\= x^{ 1 - \frac{1}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{2}{3} - (\frac{-5}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
3. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{3} - \frac{1}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{4}{5}}}{y^{1}}\\= y^{ \frac{4}{5} - 1 }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
5. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{6} - (\frac{-1}{2}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
6. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{2}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{-2}}\\= a^{ -1 - (-2) }= a^{1}\\\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-2}{3} - \frac{1}{6} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-2}{3} - \frac{2}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{3}}}{q^{-2}}\\= q^{ \frac{-1}{3} - (-2) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
12. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-2}{5} - \frac{5}{2} }= x^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ x^{29} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x^{9} }}=\frac{1}{|x^{2}|.\sqrt[10]{ x^{9} }} \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x^{3}|}\\---------------\)