Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{6}}}{x^{1}}\\= x^{ \frac{-5}{6} - 1 }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{5}{6} - (\frac{-1}{6}) }= y^{1}\\\\---------------\)
3. \(\dfrac{x^{2}}{x^{\frac{1}{5}}}\\= x^{ 2 - \frac{1}{5} }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
4. \(\dfrac{q^{\frac{5}{6}}}{q^{-2}}\\= q^{ \frac{5}{6} - (-2) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
5. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-5}{6} - (\frac{-1}{3}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
6. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-2}{5} - (\frac{-2}{3}) }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
7. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{5}{3} - \frac{1}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{1}{6}}}\\= x^{ -1 - \frac{1}{6} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{5}{2}}}\\= x^{ \frac{3}{2} - \frac{5}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
10. \(\dfrac{a^{\frac{3}{5}}}{a^{-2}}\\= a^{ \frac{3}{5} - (-2) }= a^{\frac{13}{5}}\\=\sqrt[5]{ a^{13} }=a^{2}.\sqrt[5]{ a^{3} }\\---------------\)
11. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{3}{2} - (\frac{-4}{5}) }= a^{\frac{23}{10}}\\=\sqrt[10]{ a^{23} }=|a^{2}|.\sqrt[10]{ a^{3} }\\---------------\)
12. \(\dfrac{x^{\frac{4}{3}}}{x^{1}}\\= x^{ \frac{4}{3} - 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)