Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{3} - (\frac{-1}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
2. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-4}{5} - \frac{2}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{6} - (\frac{-1}{5}) }= x^{\frac{11}{30}}\\=\sqrt[30]{ x^{11} }\\---------------\)
4. \(\dfrac{y^{-1}}{y^{\frac{-3}{2}}}\\= y^{ -1 - (\frac{-3}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
5. \(\dfrac{x^{1}}{x^{\frac{-2}{3}}}\\= x^{ 1 - (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{-1}{6}}}{a^{-1}}\\= a^{ \frac{-1}{6} - (-1) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
7. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{5}{4}}}\\= y^{ \frac{5}{4} - \frac{5}{4} }= y^{0}\\=1\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-2}{3} - \frac{3}{5} }= y^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ y^{19} }}\\=\frac{1}{y.\sqrt[15]{ y^{4} }}=\frac{1}{y.\sqrt[15]{ y^{4} }} \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{5}{3} - \frac{1}{2} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{4}}}{q^{1}}\\= q^{ \frac{-1}{4} - 1 }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{6} - (\frac{-3}{5}) }= y^{\frac{23}{30}}\\=\sqrt[30]{ y^{23} }\\---------------\)
12. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{5}{3} - (\frac{-5}{4}) }= x^{\frac{35}{12}}\\=\sqrt[12]{ x^{35} }=|x^{2}|.\sqrt[12]{ x^{11} }\\---------------\)