Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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