Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{-5}{4}}}\\= y^{ -1 - (\frac{-5}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
3. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{1}{2}}}\\= y^{ \frac{5}{6} - \frac{1}{2} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
4. \(\dfrac{a^{2}}{a^{\frac{3}{5}}}\\= a^{ 2 - \frac{3}{5} }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{5}{3} - \frac{1}{4} }= y^{\frac{17}{12}}\\=\sqrt[12]{ y^{17} }=|y|.\sqrt[12]{ y^{5} }\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{2}{5}}}\\= x^{ 1 - \frac{2}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{3} - \frac{2}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{2} - (\frac{-1}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
9. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{1}{6}}}\\= x^{ \frac{3}{2} - \frac{1}{6} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{5}{3} - (\frac{-5}{2}) }= a^{\frac{25}{6}}\\=\sqrt[6]{ a^{25} }=|a^{4}|.\sqrt[6]{ a }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)