Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{5}{6} - (\frac{-4}{5}) }= y^{\frac{49}{30}}\\=\sqrt[30]{ y^{49} }=|y|.\sqrt[30]{ y^{19} }\\---------------\)
2. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{5} - \frac{2}{3} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{6}}}\\= a^{ \frac{-1}{2} - \frac{1}{6} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
4. \(\dfrac{y^{-2}}{y^{\frac{4}{5}}}\\= y^{ -2 - \frac{4}{5} }= y^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ y^{14} }}\\=\frac{1}{y^{2}.\sqrt[5]{ y^{4} }}=\frac{1}{y^{2}.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{3}}\\---------------\)
5. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-5}{4} - (\frac{-2}{3}) }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{2} - (\frac{-2}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{a^{\frac{4}{5}}}{a^{-2}}\\= a^{ \frac{4}{5} - (-2) }= a^{\frac{14}{5}}\\=\sqrt[5]{ a^{14} }=a^{2}.\sqrt[5]{ a^{4} }\\---------------\)
8. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-3}{4} - \frac{2}{3} }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-2}{3} - (\frac{-5}{2}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{2}{3} - (\frac{-2}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{2}{3} - \frac{3}{5} }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)