Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{5}{3} - (\frac{-1}{6}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{2}{3} - \frac{1}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{5}{4}}}\\= q^{ -1 - \frac{5}{4} }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
4. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-2}{3}) }= x^{0}\\=1\\---------------\)
5. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{4}{3} - (\frac{-3}{5}) }= x^{\frac{29}{15}}\\=\sqrt[15]{ x^{29} }=x.\sqrt[15]{ x^{14} }\\---------------\)
6. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{3} - (\frac{-1}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{-1}{5}}}\\= q^{ -1 - (\frac{-1}{5}) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
8. \(\dfrac{y^{\frac{-3}{4}}}{y^{-2}}\\= y^{ \frac{-3}{4} - (-2) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
9. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{4} - (\frac{-1}{2}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{5}{6}}}{q^{-2}}\\= q^{ \frac{5}{6} - (-2) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
12. \(\dfrac{q^{1}}{q^{-2}}\\= q^{ 1 - (-2) }= q^{3}\\\\---------------\)