Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
2. \(\dfrac{y^{2}}{y^{\frac{4}{5}}}\\= y^{ 2 - \frac{4}{5} }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{1}{2} - \frac{3}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
4. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{5}{4} - (\frac{-5}{3}) }= q^{\frac{35}{12}}\\=\sqrt[12]{ q^{35} }=|q^{2}|.\sqrt[12]{ q^{11} }\\---------------\)
5. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{1}{3}}}\\= x^{ \frac{5}{4} - \frac{1}{3} }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
6. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{3} - \frac{1}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
7. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{3}{4} - \frac{1}{3} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
8. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{2}{3} - \frac{1}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{6}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{2}) }= a^{0}\\=1\\---------------\)
11. \(\dfrac{y^{2}}{y^{\frac{3}{4}}}\\= y^{ 2 - \frac{3}{4} }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
12. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{3}{2} - (\frac{-5}{6}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)