Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{3} - (\frac{-2}{5}) }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
2. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{5}{3} - \frac{4}{5} }= a^{\frac{13}{15}}\\=\sqrt[15]{ a^{13} }\\---------------\)
3. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-2}{5} - \frac{1}{3} }= y^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ y^{11} }}=\frac{1}{\sqrt[15]{ y^{11} }}. \color{purple}{\frac{\sqrt[15]{ y^{4} }}{\sqrt[15]{ y^{4} }}} \\=\frac{\sqrt[15]{ y^{4} }}{y}\\---------------\)
4. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{5}{4}}}\\= a^{ \frac{5}{6} - \frac{5}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{-1}}\\= a^{ \frac{-2}{3} - (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{1}{2}}}\\= a^{ -1 - \frac{1}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{5}{4}}}\\= q^{ \frac{1}{5} - \frac{5}{4} }= q^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ q^{21} }}\\=\frac{1}{|q|.\sqrt[20]{ q }}=\frac{1}{|q|.\sqrt[20]{ q }} \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-2}{3} - \frac{5}{2} }= x^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ x^{19} }}\\=\frac{1}{|x^{3}|.\sqrt[6]{ x }}=\frac{1}{|x^{3}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{4}|}\\---------------\)
9. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{3}{2} - (\frac{-1}{3}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{1}{5}}}\\= y^{ \frac{1}{5} - \frac{1}{5} }= y^{0}\\=1\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{-5}{4}}}\\= a^{ 1 - (\frac{-5}{4}) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-3}{4} - \frac{1}{4} }= y^{-1}\\=\frac{1}{y}\\---------------\)