Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{2} - \frac{2}{5} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{3} - \frac{5}{4} }= x^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{7} }}=\frac{1}{|x|.\sqrt[12]{ x^{7} }} \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{5}{6}}}\\= x^{ \frac{5}{3} - \frac{5}{6} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
4. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{5}{3} - \frac{1}{2} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
5. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-5}{4} - \frac{3}{4} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{2}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
7. \(\dfrac{q^{\frac{3}{4}}}{q^{2}}\\= q^{ \frac{3}{4} - 2 }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{-1}}\\= q^{ \frac{-1}{2} - (-1) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-1}{6} - \frac{4}{5} }= q^{\frac{-29}{30}}\\=\frac{1}{\sqrt[30]{ q^{29} }}=\frac{1}{\sqrt[30]{ q^{29} }}. \color{purple}{\frac{\sqrt[30]{ q }}{\sqrt[30]{ q }}} \\=\frac{\sqrt[30]{ q }}{|q|}\\---------------\)
10. \(\dfrac{a^{-1}}{a^{\frac{-4}{5}}}\\= a^{ -1 - (\frac{-4}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
11. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{2}{3} - \frac{5}{4} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
12. \(\dfrac{q^{1}}{q^{-1}}\\= q^{ 1 - (-1) }= q^{2}\\\\---------------\)