Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{2}{3} - (\frac{-3}{2}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
2. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{4} - (\frac{-1}{3}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
3. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-4}{3} - \frac{2}{3} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
4. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{3}{4} - \frac{2}{5} }= a^{\frac{7}{20}}\\=\sqrt[20]{ a^{7} }\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{4}}}\\= x^{ \frac{1}{2} - \frac{1}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
7. \(\dfrac{y^{\frac{1}{4}}}{y^{2}}\\= y^{ \frac{1}{4} - 2 }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-5}{2} - \frac{5}{6} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{1}{6}}}\\= q^{ -1 - \frac{1}{6} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{6} - \frac{1}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{3}{2} - (\frac{-1}{3}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
12. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-3}{2} - \frac{4}{3} }= x^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ x^{17} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{3}|}\\---------------\)