Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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