Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{2}{3} - (\frac{-5}{6}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
3. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{1}{4} - \frac{4}{5} }= q^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ q^{11} }}=\frac{1}{\sqrt[20]{ q^{11} }}. \color{purple}{\frac{\sqrt[20]{ q^{9} }}{\sqrt[20]{ q^{9} }}} \\=\frac{\sqrt[20]{ q^{9} }}{|q|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{2} - \frac{2}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{4} - \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
6. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-3}{5} - (\frac{-5}{2}) }= x^{\frac{19}{10}}\\=\sqrt[10]{ x^{19} }=|x|.\sqrt[10]{ x^{9} }\\---------------\)
7. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{2}{3} - \frac{2}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-1}{5} - \frac{5}{2} }= x^{\frac{-27}{10}}\\=\frac{1}{\sqrt[10]{ x^{27} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x^{7} }}=\frac{1}{|x^{2}|.\sqrt[10]{ x^{7} }} \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x^{3}|}\\---------------\)
9. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{1}{4}}}\\= q^{ \frac{3}{4} - \frac{1}{4} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-5}{4} - \frac{3}{4} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{1}{5} - (\frac{-5}{6}) }= y^{\frac{31}{30}}\\=\sqrt[30]{ y^{31} }=|y|.\sqrt[30]{ y }\\---------------\)
12. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{3}{5} - (\frac{-4}{3}) }= a^{\frac{29}{15}}\\=\sqrt[15]{ a^{29} }=a.\sqrt[15]{ a^{14} }\\---------------\)