Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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