Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{6}}}{x^{1}}\\= x^{ \frac{-5}{6} - 1 }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{2}{5} - \frac{1}{2} }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
3. \(\dfrac{q^{\frac{1}{3}}}{q^{1}}\\= q^{ \frac{1}{3} - 1 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{5}{6}}}\\= a^{ 1 - \frac{5}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{1}{5}}}{q^{-1}}\\= q^{ \frac{1}{5} - (-1) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{4}{5}}}\\= a^{ \frac{3}{5} - \frac{4}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
7. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{5}{4} - (\frac{-5}{4}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{4} - \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
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. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-2}{5} - \frac{5}{6} }= x^{\frac{-37}{30}}\\=\frac{1}{\sqrt[30]{ x^{37} }}\\=\frac{1}{|x|.\sqrt[30]{ x^{7} }}=\frac{1}{|x|.\sqrt[30]{ x^{7} }} \color{purple}{\frac{\sqrt[30]{ x^{23} }}{\sqrt[30]{ x^{23} }}} \\=\frac{\sqrt[30]{ x^{23} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{1}{5}}}\\= q^{ -1 - \frac{1}{5} }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)