Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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