Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{5} - \frac{2}{3} }= x^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ x^{7} }}=\frac{1}{\sqrt[15]{ x^{7} }}. \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x}\\---------------\)
2. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-5}{4} - (\frac{-1}{5}) }= y^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ y^{21} }}\\=\frac{1}{|y|.\sqrt[20]{ y }}=\frac{1}{|y|.\sqrt[20]{ y }} \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-1}{3} - \frac{5}{2} }= x^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ x^{17} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{3}|}\\---------------\)
4. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-4}{3} - (\frac{-1}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
5. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{5} - \frac{1}{2} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
6. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{3}{4} - (\frac{-3}{4}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
7. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
8. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{5} - (\frac{-1}{3}) }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{-1}{3}}}\\= x^{ 1 - (\frac{-1}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{-5}{3}}}\\= x^{ 1 - (\frac{-5}{3}) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-1}{6} - (\frac{-5}{3}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
12. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{4}{3} - (\frac{-1}{2}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)