Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{1}{2} - (\frac{-1}{6}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
2. \(\dfrac{y^{2}}{y^{\frac{1}{2}}}\\= y^{ 2 - \frac{1}{2} }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
3. \(\dfrac{x^{\frac{-2}{3}}}{x^{-1}}\\= x^{ \frac{-2}{3} - (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{4}{5}}}\\= q^{ 1 - \frac{4}{5} }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
5. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{3}{4} - \frac{1}{3} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
6. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{4}{3} - (\frac{-5}{6}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
8. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{3}}}\\= q^{ \frac{1}{4} - \frac{5}{3} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{5}{6}}}\\= x^{ -1 - \frac{5}{6} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
10. \(\dfrac{q^{2}}{q^{\frac{-5}{4}}}\\= q^{ 2 - (\frac{-5}{4}) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)
11. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{5}{6}}}\\= q^{ \frac{1}{6} - \frac{5}{6} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
12. \(\dfrac{q^{\frac{2}{3}}}{q^{1}}\\= q^{ \frac{2}{3} - 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)