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

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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. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{4}{5} - (\frac{-1}{3}) }= q^{\frac{17}{15}}\\=\sqrt[15]{ q^{17} }=q.\sqrt[15]{ q^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-4}{3} - \frac{1}{4} }= q^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{7} }}=\frac{1}{|q|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{3}{5} - \frac{5}{2} }= a^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{9} }}=\frac{1}{|a|.\sqrt[10]{ a^{9} }} \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{2}{5}}}{q^{-1}}\\= q^{ \frac{2}{5} - (-1) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{2} - (\frac{-5}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{6}}}\\= x^{ \frac{2}{3} - \frac{1}{6} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{-5}{3}}}\\= x^{ -1 - (\frac{-5}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
9. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{4}{3} - \frac{5}{2} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{4}{5} - (\frac{-5}{6}) }= a^{\frac{49}{30}}\\=\sqrt[30]{ a^{49} }=|a|.\sqrt[30]{ a^{19} }\\---------------\)
11. \(\dfrac{q^{-2}}{q^{\frac{-5}{6}}}\\= q^{ -2 - (\frac{-5}{6}) }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{4}{3}}}\\= x^{ -1 - \frac{4}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)