Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-1}{5} - (\frac{-3}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{-5}{3}}}\\= y^{ -1 - (\frac{-5}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{-3}{5}}}\\= q^{ -1 - (\frac{-3}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
4. \(\dfrac{x^{\frac{-5}{6}}}{x^{-1}}\\= x^{ \frac{-5}{6} - (-1) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
5. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-2}{3} - \frac{2}{5} }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{3}{5}}}\\= y^{ 1 - \frac{3}{5} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{6}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{2} - \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
9. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{4}{3} - (\frac{-2}{5}) }= q^{\frac{26}{15}}\\=\sqrt[15]{ q^{26} }=q.\sqrt[15]{ q^{11} }\\---------------\)
10. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-5}{6} - \frac{3}{5} }= a^{\frac{-43}{30}}\\=\frac{1}{\sqrt[30]{ a^{43} }}\\=\frac{1}{|a|.\sqrt[30]{ a^{13} }}=\frac{1}{|a|.\sqrt[30]{ a^{13} }} \color{purple}{\frac{\sqrt[30]{ a^{17} }}{\sqrt[30]{ a^{17} }}} \\=\frac{\sqrt[30]{ a^{17} }}{|a^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-2}{5} - \frac{5}{3} }= y^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ y^{31} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y }}=\frac{1}{y^{2}.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{3}}\\---------------\)
12. \(\dfrac{q^{\frac{5}{6}}}{q^{-2}}\\= q^{ \frac{5}{6} - (-2) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)