Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{4}{3} - (\frac{-1}{4}) }= a^{\frac{19}{12}}\\=\sqrt[12]{ a^{19} }=|a|.\sqrt[12]{ a^{7} }\\---------------\)
2. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{5} - \frac{1}{3} }= a^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ a^{14} }}=\frac{1}{\sqrt[15]{ a^{14} }}. \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{2} - \frac{1}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{2}{3} - (\frac{-1}{3}) }= q^{1}\\\\---------------\)
6. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{5}{4} - (\frac{-4}{5}) }= x^{\frac{41}{20}}\\=\sqrt[20]{ x^{41} }=|x^{2}|.\sqrt[20]{ x }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{-3}{2}}}{q^{-1}}\\= q^{ \frac{-3}{2} - (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-5}{4} - (\frac{-5}{6}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
10. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-5}{2} - \frac{3}{4} }= x^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ x^{13} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x }}=\frac{1}{|x^{3}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{4}|}\\---------------\)
11. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{2}{5} - (\frac{-1}{3}) }= q^{\frac{11}{15}}\\=\sqrt[15]{ q^{11} }\\---------------\)
12. \(\dfrac{y^{2}}{y^{\frac{4}{5}}}\\= y^{ 2 - \frac{4}{5} }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)