Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{6} - (\frac{-1}{2}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{1}{2} - (\frac{-3}{2}) }= q^{2}\\\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{2} - \frac{2}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
4. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{4} - (\frac{-2}{5}) }= y^{\frac{13}{20}}\\=\sqrt[20]{ y^{13} }\\---------------\)
5. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{2}{3} - \frac{2}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
6. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
7. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{2} - \frac{2}{3} }= y^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ y^{19} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y }}=\frac{1}{|y^{3}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{4}|}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{3} - \frac{2}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{4}{5} - (\frac{-5}{6}) }= a^{\frac{49}{30}}\\=\sqrt[30]{ a^{49} }=|a|.\sqrt[30]{ a^{19} }\\---------------\)
10. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{3}{4} - (\frac{-1}{6}) }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{4}{3}}}\\= a^{ \frac{1}{6} - \frac{4}{3} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{3} - \frac{5}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)