Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-2}}{q^{\frac{1}{2}}}\\= q^{ -2 - \frac{1}{2} }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
2. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{5}{3} - \frac{5}{3} }= q^{0}\\=1\\---------------\)
3. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-3}{2} - \frac{4}{3} }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{3}{5}}}\\= a^{ \frac{1}{5} - \frac{3}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{6}}}\\= q^{ \frac{1}{4} - \frac{5}{6} }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{2} - \frac{2}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{3}{2}}}\\= a^{ -1 - \frac{3}{2} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-3}{4}}}\\= y^{ 1 - (\frac{-3}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{-3}{5}}}\\= q^{ -1 - (\frac{-3}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
10. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-2}{3} - \frac{1}{4} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-5}{4} - (\frac{-1}{6}) }= x^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[12]{ x }}=\frac{1}{|x|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{y^{-2}}{y^{\frac{4}{3}}}\\= y^{ -2 - \frac{4}{3} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)