Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{2}}{x^{1}}\\= x^{ 2 - 1 }= x^{1}\\\\---------------\)
2. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-2}{3} - \frac{5}{6} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-1}{4} - (\frac{-1}{4}) }= q^{0}\\=1\\---------------\)
4. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{5}{4} - \frac{1}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{-2}}\\= y^{ \frac{1}{2} - (-2) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-1}{3} - \frac{3}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{3} - \frac{2}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{5}}}{x^{-1}}\\= x^{ \frac{-1}{5} - (-1) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
9. \(\dfrac{x^{2}}{x^{\frac{1}{2}}}\\= x^{ 2 - \frac{1}{2} }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
10. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{5}{3} - (\frac{-1}{5}) }= x^{\frac{28}{15}}\\=\sqrt[15]{ x^{28} }=x.\sqrt[15]{ x^{13} }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{6}}}{x^{-1}}\\= x^{ \frac{-1}{6} - (-1) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
12. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{5}{2}}}\\= a^{ \frac{1}{4} - \frac{5}{2} }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)