Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{3}{5} - (\frac{-1}{3}) }= x^{\frac{14}{15}}\\=\sqrt[15]{ x^{14} }\\---------------\)
2. \(\dfrac{x^{\frac{5}{6}}}{x^{-2}}\\= x^{ \frac{5}{6} - (-2) }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)
3. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{3}{2} - (\frac{-1}{3}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{2}) }= a^{1}\\\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{2} - \frac{5}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{2} - \frac{2}{3} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-1}{3} - \frac{2}{5} }= a^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ a^{11} }}=\frac{1}{\sqrt[15]{ a^{11} }}. \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a}\\---------------\)
8. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{4}{3} - \frac{1}{3} }= y^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{-1}}\\= q^{ \frac{-1}{3} - (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
10. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{5}{3} - (\frac{-2}{5}) }= a^{\frac{31}{15}}\\=\sqrt[15]{ a^{31} }=a^{2}.\sqrt[15]{ a }\\---------------\)
11. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{1}{5} - \frac{5}{6} }= y^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ y^{19} }}=\frac{1}{\sqrt[30]{ y^{19} }}. \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y|}\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)