Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-5}{2} - \frac{5}{6} }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)
2. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{5}{4}}}\\= a^{ \frac{1}{5} - \frac{5}{4} }= a^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ a^{21} }}\\=\frac{1}{|a|.\sqrt[20]{ a }}=\frac{1}{|a|.\sqrt[20]{ a }} \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{1}{5}}}{y^{-1}}\\= y^{ \frac{1}{5} - (-1) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{3} - \frac{3}{2} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{4} - \frac{1}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{1}{3} - (\frac{-4}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{2}{3} - (\frac{-5}{6}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
8. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{3}{5} - \frac{3}{2} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{1}{6} - (\frac{-2}{5}) }= a^{\frac{17}{30}}\\=\sqrt[30]{ a^{17} }\\---------------\)
10. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{6} - (\frac{-2}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{2} - \frac{1}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{1}{2} - (\frac{-4}{3}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)