Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{1}{2}}}\\= x^{ \frac{5}{6} - \frac{1}{2} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
2. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-2}{3} - \frac{1}{2} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-1}{6} - \frac{5}{6} }= x^{-1}\\=\frac{1}{x}\\---------------\)
4. \(\dfrac{a^{2}}{a^{1}}\\= a^{ 2 - 1 }= a^{1}\\\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{2}{5}}}\\= y^{ 1 - \frac{2}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
6. \(\dfrac{q^{\frac{-5}{3}}}{q^{1}}\\= q^{ \frac{-5}{3} - 1 }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
7. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{2}{5} - (\frac{-4}{5}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{4}{5} - (\frac{-5}{3}) }= x^{\frac{37}{15}}\\=\sqrt[15]{ x^{37} }=x^{2}.\sqrt[15]{ x^{7} }\\---------------\)
10. \(\dfrac{a^{-1}}{a^{\frac{-5}{3}}}\\= a^{ -1 - (\frac{-5}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
11. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{3} - (\frac{-1}{6}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
12. \(\dfrac{q^{\frac{1}{3}}}{q^{1}}\\= q^{ \frac{1}{3} - 1 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)