Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{5}{6} - (\frac{-2}{3}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
2. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-3}{5} - \frac{2}{3} }= q^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ q^{19} }}\\=\frac{1}{q.\sqrt[15]{ q^{4} }}=\frac{1}{q.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{5}{3}}}{y^{-1}}\\= y^{ \frac{5}{3} - (-1) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-5}{2} - (\frac{-2}{3}) }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
5. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{4}{3} - \frac{1}{3} }= y^{1}\\\\---------------\)
7. \(\dfrac{x^{\frac{3}{5}}}{x^{-2}}\\= x^{ \frac{3}{5} - (-2) }= x^{\frac{13}{5}}\\=\sqrt[5]{ x^{13} }=x^{2}.\sqrt[5]{ x^{3} }\\---------------\)
8. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{2} - \frac{1}{3} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
9. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{2}{5} - \frac{5}{6} }= y^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ y^{13} }}=\frac{1}{\sqrt[30]{ y^{13} }}. \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y|}\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
11. \(\dfrac{x^{2}}{x^{2}}\\= x^{ 2 - 2 }= x^{0}\\=1\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{2} - \frac{3}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)