Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-5}{3} - \frac{3}{2} }= x^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ x^{19} }}\\=\frac{1}{|x^{3}|.\sqrt[6]{ x }}=\frac{1}{|x^{3}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{4}|}\\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{2}{3} - (\frac{-5}{2}) }= x^{\frac{19}{6}}\\=\sqrt[6]{ x^{19} }=|x^{3}|.\sqrt[6]{ x }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{1}{4}}}\\= q^{ -1 - \frac{1}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-1}{6} - \frac{5}{4} }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-2}{3} - \frac{1}{5} }= q^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ q^{13} }}=\frac{1}{\sqrt[15]{ q^{13} }}. \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q}\\---------------\)
7. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{3}{2} - (\frac{-1}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
8. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-3}{4} - \frac{1}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{4} - (\frac{-1}{2}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
10. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{4}}}\\= q^{ \frac{5}{6} - \frac{5}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
11. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-3}{4} - (\frac{-3}{5}) }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)