Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-3}{4} - (\frac{-1}{2}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{2}{3} - \frac{5}{6} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{5} - \frac{2}{3} }= x^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ x^{7} }}=\frac{1}{\sqrt[15]{ x^{7} }}. \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{2} - \frac{1}{2} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
5. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{5}{4} - \frac{1}{2} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
6. \(\dfrac{a^{\frac{5}{2}}}{a^{-1}}\\= a^{ \frac{5}{2} - (-1) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
7. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
8. \(\dfrac{a^{-1}}{a^{\frac{-1}{4}}}\\= a^{ -1 - (\frac{-1}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
9. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{5}{3} - \frac{5}{3} }= q^{0}\\=1\\---------------\)
10. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-4}{5} - \frac{5}{6} }= x^{\frac{-49}{30}}\\=\frac{1}{\sqrt[30]{ x^{49} }}\\=\frac{1}{|x|.\sqrt[30]{ x^{19} }}=\frac{1}{|x|.\sqrt[30]{ x^{19} }} \color{purple}{\frac{\sqrt[30]{ x^{11} }}{\sqrt[30]{ x^{11} }}} \\=\frac{\sqrt[30]{ x^{11} }}{|x^{2}|}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{-4}{3}}}\\= y^{ -1 - (\frac{-4}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{4} - (\frac{-2}{3}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)