Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{2}{3} - (\frac{-1}{3}) }= a^{1}\\\\---------------\)
2. \(\dfrac{a^{2}}{a^{\frac{-2}{3}}}\\= a^{ 2 - (\frac{-2}{3}) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{3}{4} - \frac{1}{2} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
4. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{2}{3} - \frac{2}{3} }= x^{0}\\=1\\---------------\)
5. \(\dfrac{y^{\frac{5}{2}}}{y^{-1}}\\= y^{ \frac{5}{2} - (-1) }= y^{\frac{7}{2}}\\= \sqrt{ y^{7} } =|y^{3}|. \sqrt{ y } \\---------------\)
6. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{4}{5} - (\frac{-5}{4}) }= x^{\frac{41}{20}}\\=\sqrt[20]{ x^{41} }=|x^{2}|.\sqrt[20]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-5}{3} - \frac{5}{6} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
8. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{6} - (\frac{-1}{2}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-2}{3} - (\frac{-5}{2}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{-2}{5}}}\\= q^{ -1 - (\frac{-2}{5}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
11. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{4} - (\frac{-5}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
12. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-3}{4} - (\frac{-4}{3}) }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)