Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{2}{3} - (\frac{-5}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{3} - (\frac{-1}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{5}{4}}}\\= x^{ -1 - \frac{5}{4} }= x^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ x^{9} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x }}=\frac{1}{|x^{2}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{3}|}\\---------------\)
4. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-4}{5} - (\frac{-5}{6}) }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)
5. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{5}{6} - (\frac{-5}{4}) }= q^{\frac{25}{12}}\\=\sqrt[12]{ q^{25} }=|q^{2}|.\sqrt[12]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{4}{5} - \frac{1}{3} }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
7. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{5}{2} - (\frac{-3}{2}) }= x^{4}\\\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{1}{2} - (\frac{-1}{5}) }= y^{\frac{7}{10}}\\=\sqrt[10]{ y^{7} }\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{-3}{2}}}\\= a^{ 1 - (\frac{-3}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
10. \(\dfrac{y^{\frac{1}{5}}}{y^{1}}\\= y^{ \frac{1}{5} - 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{3}{4}}}\\= q^{ 1 - \frac{3}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{3}{5} - (\frac{-4}{5}) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)