Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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