Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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