Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-2}}{a^{\frac{3}{4}}}\\= a^{ -2 - \frac{3}{4} }= a^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ a^{11} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }}=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{3}|}\\---------------\)
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. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{2}{5} - (\frac{-3}{5}) }= y^{1}\\\\---------------\)
4. \(\dfrac{x^{\frac{3}{5}}}{x^{-1}}\\= x^{ \frac{3}{5} - (-1) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
5. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
6. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{1}{4} - (\frac{-1}{5}) }= q^{\frac{9}{20}}\\=\sqrt[20]{ q^{9} }\\---------------\)
7. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{6} - (\frac{-3}{4}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{1}{2} - \frac{4}{5} }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
9. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{2}{5} - (\frac{-3}{2}) }= y^{\frac{19}{10}}\\=\sqrt[10]{ y^{19} }=|y|.\sqrt[10]{ y^{9} }\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
11. \(\dfrac{x^{\frac{5}{6}}}{x^{-1}}\\= x^{ \frac{5}{6} - (-1) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{1}{6}}}\\= a^{ 1 - \frac{1}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)