Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{3}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
2. \(\dfrac{y^{\frac{5}{3}}}{y^{-2}}\\= y^{ \frac{5}{3} - (-2) }= y^{\frac{11}{3}}\\=\sqrt[3]{ y^{11} }=y^{3}.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{2}{3} - \frac{4}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-1}{2} - \frac{5}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
5. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-1}{2} - (\frac{-4}{5}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
7. \(\dfrac{a^{\frac{-3}{5}}}{a^{-1}}\\= a^{ \frac{-3}{5} - (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
8. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{1}{6}}}\\= y^{ \frac{5}{6} - \frac{1}{6} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{2}{5}}}\\= y^{ -1 - \frac{2}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{3} - (\frac{-2}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{2}{5} - (\frac{-4}{3}) }= y^{\frac{26}{15}}\\=\sqrt[15]{ y^{26} }=y.\sqrt[15]{ y^{11} }\\---------------\)