Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{2}}{a^{1}}\\= a^{ 2 - 1 }= a^{1}\\\\---------------\)
2. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{5}{2}}}\\= y^{ \frac{4}{5} - \frac{5}{2} }= y^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{7} }}=\frac{1}{|y|.\sqrt[10]{ y^{7} }} \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y^{2}|}\\---------------\)
3. \(\dfrac{a^{2}}{a^{\frac{-4}{5}}}\\= a^{ 2 - (\frac{-4}{5}) }= a^{\frac{14}{5}}\\=\sqrt[5]{ a^{14} }=a^{2}.\sqrt[5]{ a^{4} }\\---------------\)
4. \(\dfrac{x^{1}}{x^{\frac{2}{5}}}\\= x^{ 1 - \frac{2}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
5. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{4} - (\frac{-1}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
6. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{6} - (\frac{-2}{5}) }= a^{\frac{7}{30}}\\=\sqrt[30]{ a^{7} }\\---------------\)
7. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{1}{5} - (\frac{-5}{3}) }= q^{\frac{28}{15}}\\=\sqrt[15]{ q^{28} }=q.\sqrt[15]{ q^{13} }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{2} - \frac{1}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
9. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-2}{3} - \frac{5}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
10. \(\dfrac{y^{-2}}{y^{\frac{1}{2}}}\\= y^{ -2 - \frac{1}{2} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
11. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{2}{3} - \frac{1}{2} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{2} - (\frac{-1}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)