Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{-5}{4}}}\\= q^{ -1 - (\frac{-5}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{2}{5} - (\frac{-1}{4}) }= q^{\frac{13}{20}}\\=\sqrt[20]{ q^{13} }\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{1}{2} - \frac{2}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{q^{\frac{4}{3}}}{q^{-1}}\\= q^{ \frac{4}{3} - (-1) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
7. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{6} - (\frac{-5}{2}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-3}{2} - \frac{1}{2} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{2}{5}}}\\= x^{ -1 - \frac{2}{5} }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
10. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{3}{2} - (\frac{-4}{3}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
11. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-3}{5} - (\frac{-3}{2}) }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{1}{3}}}\\= y^{ 1 - \frac{1}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)