Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-4}{5} - (\frac{-5}{6}) }= y^{\frac{1}{30}}\\=\sqrt[30]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-5}{3} - (\frac{-3}{5}) }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{4} - \frac{2}{5} }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
4. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-5}{6} - \frac{2}{3} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{-1}{4}}}\\= y^{ 1 - (\frac{-1}{4}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{1}{2} - (\frac{-4}{3}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
7. \(\dfrac{x^{\frac{5}{2}}}{x^{-2}}\\= x^{ \frac{5}{2} - (-2) }= x^{\frac{9}{2}}\\= \sqrt{ x^{9} } =|x^{4}|. \sqrt{ x } \\---------------\)
8. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{3}{5} - \frac{2}{3} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
9. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-4}{5} - (\frac{-3}{2}) }= a^{\frac{7}{10}}\\=\sqrt[10]{ a^{7} }\\---------------\)
10. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)
11. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-4}{5} - \frac{1}{4} }= y^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ y^{21} }}\\=\frac{1}{|y|.\sqrt[20]{ y }}=\frac{1}{|y|.\sqrt[20]{ y }} \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{2} - \frac{1}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)