Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{3}{4} - (\frac{-4}{5}) }= x^{\frac{31}{20}}\\=\sqrt[20]{ x^{31} }=|x|.\sqrt[20]{ x^{11} }\\---------------\)
2. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{5}{3} - \frac{1}{2} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
3. \(\dfrac{x^{\frac{-3}{5}}}{x^{-1}}\\= x^{ \frac{-3}{5} - (-1) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{4}{5} - \frac{1}{6} }= y^{\frac{19}{30}}\\=\sqrt[30]{ y^{19} }\\---------------\)
5. \(\dfrac{a^{\frac{1}{6}}}{a^{-1}}\\= a^{ \frac{1}{6} - (-1) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
6. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-4}{3} - \frac{1}{2} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{5}{4} - (\frac{-4}{5}) }= q^{\frac{41}{20}}\\=\sqrt[20]{ q^{41} }=|q^{2}|.\sqrt[20]{ q }\\---------------\)
8. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-2}{3} - (\frac{-3}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-2}{5} - (\frac{-2}{3}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
10. \(\dfrac{a^{\frac{-3}{4}}}{a^{-1}}\\= a^{ \frac{-3}{4} - (-1) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{5}{2}}}\\= x^{ 1 - \frac{5}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{3}{5}}}\\= a^{ -1 - \frac{3}{5} }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)