Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-3}{4} - \frac{1}{3} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{1}}\\= a^{ \frac{2}{3} - 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-1}{3} - \frac{3}{5} }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
5. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-5}{3} - \frac{4}{5} }= q^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ q^{37} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }}=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{3}}\\---------------\)
6. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-2}{3} - \frac{1}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
7. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{1}{6}}}\\= q^{ \frac{5}{6} - \frac{1}{6} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{6}}}\\= a^{ \frac{5}{4} - \frac{1}{6} }= a^{\frac{13}{12}}\\=\sqrt[12]{ a^{13} }=|a|.\sqrt[12]{ a }\\---------------\)
9. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{5}{2} - \frac{5}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{4}{3}}}\\= x^{ \frac{3}{5} - \frac{4}{3} }= x^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ x^{11} }}=\frac{1}{\sqrt[15]{ x^{11} }}. \color{purple}{\frac{\sqrt[15]{ x^{4} }}{\sqrt[15]{ x^{4} }}} \\=\frac{\sqrt[15]{ x^{4} }}{x}\\---------------\)
12. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{5}{2} - \frac{2}{5} }= x^{\frac{21}{10}}\\=\sqrt[10]{ x^{21} }=|x^{2}|.\sqrt[10]{ x }\\---------------\)