Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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