Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{6} - \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\dfrac{y^{\frac{-2}{5}}}{y^{-1}}\\= y^{ \frac{-2}{5} - (-1) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
3. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{3}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{x^{1}}{x^{\frac{-1}{3}}}\\= x^{ 1 - (\frac{-1}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
5. \(\dfrac{q^{1}}{q^{-1}}\\= q^{ 1 - (-1) }= q^{2}\\\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{-4}{5}}}\\= a^{ 1 - (\frac{-4}{5}) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-1}{6} - \frac{2}{5} }= q^{\frac{-17}{30}}\\=\frac{1}{\sqrt[30]{ q^{17} }}=\frac{1}{\sqrt[30]{ q^{17} }}. \color{purple}{\frac{\sqrt[30]{ q^{13} }}{\sqrt[30]{ q^{13} }}} \\=\frac{\sqrt[30]{ q^{13} }}{|q|}\\---------------\)
8. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{5}{3} - \frac{1}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
9. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-2}{3} - \frac{2}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
10. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{2}{3} - \frac{1}{4} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-2}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
12. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{3}{5} - (\frac{-5}{3}) }= q^{\frac{34}{15}}\\=\sqrt[15]{ q^{34} }=q^{2}.\sqrt[15]{ q^{4} }\\---------------\)