Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{\frac{3}{4}}}\\= a^{ -1 - \frac{3}{4} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{2} - \frac{5}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-4}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{1}{4} - (\frac{-5}{3}) }= q^{\frac{23}{12}}\\=\sqrt[12]{ q^{23} }=|q|.\sqrt[12]{ q^{11} }\\---------------\)
5. \(\dfrac{q^{\frac{5}{6}}}{q^{-2}}\\= q^{ \frac{5}{6} - (-2) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
6. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{4}{3}}}\\= x^{ \frac{5}{2} - \frac{4}{3} }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
7. \(\dfrac{x^{1}}{x^{-2}}\\= x^{ 1 - (-2) }= x^{3}\\\\---------------\)
8. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{4} - (\frac{-1}{3}) }= y^{\frac{19}{12}}\\=\sqrt[12]{ y^{19} }=|y|.\sqrt[12]{ y^{7} }\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{1}{2}}}\\= a^{ -1 - \frac{1}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{5} - (\frac{-1}{2}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
11. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-4}{3} - \frac{3}{4} }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-3}{2}) }= y^{1}\\\\---------------\)