Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{3} - (\frac{-2}{3}) }= y^{1}\\\\---------------\)
2. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{5} - \frac{1}{2} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
3. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-4}{5} - \frac{3}{4} }= a^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ a^{31} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{11} }}=\frac{1}{|a|.\sqrt[20]{ a^{11} }} \color{purple}{\frac{\sqrt[20]{ a^{9} }}{\sqrt[20]{ a^{9} }}} \\=\frac{\sqrt[20]{ a^{9} }}{|a^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-2}{5}}}{y^{-1}}\\= y^{ \frac{-2}{5} - (-1) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
5. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-5}{3}) }= x^{1}\\\\---------------\)
6. \(\dfrac{q^{\frac{2}{3}}}{q^{1}}\\= q^{ \frac{2}{3} - 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-5}{6} - \frac{1}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{y^{1}}{y^{-2}}\\= y^{ 1 - (-2) }= y^{3}\\\\---------------\)
9. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{5} - (\frac{-1}{3}) }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{2}{3} - \frac{2}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
11. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{1}{6} - (\frac{-3}{5}) }= x^{\frac{23}{30}}\\=\sqrt[30]{ x^{23} }\\---------------\)
12. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-5}{4} - \frac{3}{2} }= x^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ x^{11} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x^{3} }}=\frac{1}{|x^{2}|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{3}|}\\---------------\)