Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{2}{5} - (\frac{-1}{5}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
2. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-4}{3} - \frac{3}{4} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
3. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-2}{5} - \frac{1}{3} }= a^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ a^{11} }}=\frac{1}{\sqrt[15]{ a^{11} }}. \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a}\\---------------\)
4. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{2} - (\frac{-2}{3}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{2}{3} - (\frac{-2}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{5}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
7. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{2}{5} - (\frac{-4}{3}) }= x^{\frac{26}{15}}\\=\sqrt[15]{ x^{26} }=x.\sqrt[15]{ x^{11} }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
9. \(\dfrac{a^{\frac{4}{3}}}{a^{1}}\\= a^{ \frac{4}{3} - 1 }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{2}{5} - (\frac{-1}{6}) }= a^{\frac{17}{30}}\\=\sqrt[30]{ a^{17} }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{6}}}{a^{2}}\\= a^{ \frac{-1}{6} - 2 }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
12. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-3}{5} - \frac{1}{2} }= q^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[10]{ q }}=\frac{1}{|q|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{2}|}\\---------------\)