Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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