Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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