Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{6} - (\frac{-5}{4}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
2. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-2}{5} - (\frac{-3}{2}) }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{-4}{5}}}\\= y^{ 1 - (\frac{-4}{5}) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)
4. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-4}{3} - (\frac{-2}{5}) }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{3}{2} - (\frac{-2}{5}) }= x^{\frac{19}{10}}\\=\sqrt[10]{ x^{19} }=|x|.\sqrt[10]{ x^{9} }\\---------------\)
6. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
7. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{6} - \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\dfrac{q^{\frac{5}{6}}}{q^{-2}}\\= q^{ \frac{5}{6} - (-2) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
9. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{5}{3} - (\frac{-1}{3}) }= x^{2}\\\\---------------\)
10. \(\dfrac{x^{\frac{2}{3}}}{x^{1}}\\= x^{ \frac{2}{3} - 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-5}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
12. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{4} - (\frac{-1}{2}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)