Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{3}{4} - \frac{1}{2} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
2. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{-1}{3}}}\\= q^{ -1 - (\frac{-1}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-2}{3} - \frac{5}{2} }= y^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ y^{19} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y }}=\frac{1}{|y^{3}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{4}|}\\---------------\)
5. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{4}{5} - \frac{1}{3} }= a^{\frac{7}{15}}\\=\sqrt[15]{ a^{7} }\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{1}{3} - \frac{5}{6} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-5}{4} - (\frac{-1}{3}) }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
8. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-2}{5} - (\frac{-5}{2}) }= a^{\frac{21}{10}}\\=\sqrt[10]{ a^{21} }=|a^{2}|.\sqrt[10]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{3}{2}}}{x^{-2}}\\= x^{ \frac{3}{2} - (-2) }= x^{\frac{7}{2}}\\= \sqrt{ x^{7} } =|x^{3}|. \sqrt{ x } \\---------------\)
10. \(\dfrac{a^{\frac{-3}{4}}}{a^{-1}}\\= a^{ \frac{-3}{4} - (-1) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{2}{3} - (\frac{-2}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)