Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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