Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{4}}}{x^{-1}}\\= x^{ \frac{5}{4} - (-1) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
2. \(\dfrac{a^{\frac{-5}{3}}}{a^{1}}\\= a^{ \frac{-5}{3} - 1 }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
3. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{4}}}\\= q^{ \frac{1}{4} - \frac{5}{4} }= q^{-1}\\=\frac{1}{q}\\---------------\)
4. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{5}{2} - (\frac{-1}{5}) }= y^{\frac{27}{10}}\\=\sqrt[10]{ y^{27} }=|y^{2}|.\sqrt[10]{ y^{7} }\\---------------\)
5. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{2}{5} - (\frac{-1}{3}) }= x^{\frac{11}{15}}\\=\sqrt[15]{ x^{11} }\\---------------\)
6. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{3} - (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{2} - \frac{2}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{5} - \frac{1}{3} }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
10. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{1}{5} - (\frac{-3}{2}) }= x^{\frac{17}{10}}\\=\sqrt[10]{ x^{17} }=|x|.\sqrt[10]{ x^{7} }\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{1}{6}}}\\= q^{ 1 - \frac{1}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
12. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{3}{2}}}\\= a^{ \frac{3}{4} - \frac{3}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)