Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{-5}{4}}}\\= q^{ 1 - (\frac{-5}{4}) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
2. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{2} - \frac{2}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{5}}}\\= y^{ \frac{3}{4} - \frac{1}{5} }= y^{\frac{11}{20}}\\=\sqrt[20]{ y^{11} }\\---------------\)
4. \(\dfrac{y^{\frac{-1}{6}}}{y^{-1}}\\= y^{ \frac{-1}{6} - (-1) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
5. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-2}{3} - (\frac{-3}{5}) }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{1}{6}}}\\= x^{ -1 - \frac{1}{6} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-3}{5} - (\frac{-4}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
9. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{1}{3} - (\frac{-5}{3}) }= a^{2}\\\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-2}{3} - \frac{3}{4} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{4}{5} - (\frac{-1}{3}) }= y^{\frac{17}{15}}\\=\sqrt[15]{ y^{17} }=y.\sqrt[15]{ y^{2} }\\---------------\)