Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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