Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{2}{3}}}\\= a^{ 1 - \frac{2}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{2} - \frac{1}{2} }= y^{0}\\=1\\---------------\)
3. \(\dfrac{x^{1}}{x^{\frac{2}{5}}}\\= x^{ 1 - \frac{2}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
4. \(\dfrac{q^{-1}}{q^{\frac{1}{6}}}\\= q^{ -1 - \frac{1}{6} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{5} - \frac{3}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
7. \(\dfrac{x^{\frac{-2}{5}}}{x^{1}}\\= x^{ \frac{-2}{5} - 1 }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{-5}{2}}}\\= q^{ 1 - (\frac{-5}{2}) }= q^{\frac{7}{2}}\\= \sqrt{ q^{7} } =|q^{3}|. \sqrt{ q } \\---------------\)
9. \(\dfrac{x^{\frac{-5}{6}}}{x^{-2}}\\= x^{ \frac{-5}{6} - (-2) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-1}{2} - \frac{4}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{-1}}\\= q^{ \frac{-1}{2} - (-1) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)