Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-2}{3} - \frac{1}{4} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{2}{5} - (\frac{-1}{6}) }= q^{\frac{17}{30}}\\=\sqrt[30]{ q^{17} }\\---------------\)
3. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{1}{4} - (\frac{-4}{3}) }= a^{\frac{19}{12}}\\=\sqrt[12]{ a^{19} }=|a|.\sqrt[12]{ a^{7} }\\---------------\)
4. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-2}{5} - \frac{5}{3} }= y^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ y^{31} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y }}=\frac{1}{y^{2}.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{3}}\\---------------\)
5. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-2}{3} - \frac{2}{5} }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{4}{3} - (\frac{-2}{5}) }= q^{\frac{26}{15}}\\=\sqrt[15]{ q^{26} }=q.\sqrt[15]{ q^{11} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{4} - \frac{1}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-5}{4}}}\\= y^{ 1 - (\frac{-5}{4}) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
9. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{6} - (\frac{-2}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{1}{4}}}\\= x^{ -1 - \frac{1}{4} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{5} - (\frac{-5}{6}) }= a^{\frac{19}{30}}\\=\sqrt[30]{ a^{19} }\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)