Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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