Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-2}}{q^{\frac{1}{2}}}\\= q^{ -2 - \frac{1}{2} }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{1}{5}}}{a^{2}}\\= a^{ \frac{1}{5} - 2 }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{3}{5} - (\frac{-2}{3}) }= x^{\frac{19}{15}}\\=\sqrt[15]{ x^{19} }=x.\sqrt[15]{ x^{4} }\\---------------\)
4. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{1}{5} - (\frac{-4}{3}) }= y^{\frac{23}{15}}\\=\sqrt[15]{ y^{23} }=y.\sqrt[15]{ y^{8} }\\---------------\)
5. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{-2}{3}}}\\= a^{ 1 - (\frac{-2}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{-5}{6}}}\\= y^{ 1 - (\frac{-5}{6}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{-1}{5}}}\\= q^{ 1 - (\frac{-1}{5}) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{6} - (\frac{-1}{2}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{1}{3}}}\\= a^{ 1 - \frac{1}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{2} - \frac{1}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)