Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{2}{3} - \frac{1}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{4} - \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
3. \(\dfrac{x^{1}}{x^{\frac{1}{6}}}\\= x^{ 1 - \frac{1}{6} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
4. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{5}{3} - (\frac{-2}{5}) }= q^{\frac{31}{15}}\\=\sqrt[15]{ q^{31} }=q^{2}.\sqrt[15]{ q }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{2} - \frac{1}{4} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{2}}\\= x^{ \frac{2}{3} - 2 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-3}{4} - \frac{2}{3} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{2}{3} - \frac{3}{4} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
11. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-5}{4} - \frac{5}{6} }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
12. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-4}{5} - \frac{5}{4} }= a^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ a^{41} }}\\=\frac{1}{|a^{2}|.\sqrt[20]{ a }}=\frac{1}{|a^{2}|.\sqrt[20]{ a }} \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a^{3}|}\\---------------\)