Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-3}{5} - \frac{2}{5} }= y^{-1}\\=\frac{1}{y}\\---------------\)
2. \(\dfrac{x^{\frac{1}{5}}}{x^{1}}\\= x^{ \frac{1}{5} - 1 }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
3. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{2}{3} - (\frac{-1}{6}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
5. \(\dfrac{a^{-1}}{a^{\frac{5}{2}}}\\= a^{ -1 - \frac{5}{2} }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{1}{3} - (\frac{-5}{6}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
7. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{4}{5} - (\frac{-5}{2}) }= x^{\frac{33}{10}}\\=\sqrt[10]{ x^{33} }=|x^{3}|.\sqrt[10]{ x^{3} }\\---------------\)
8. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{5}{2} - (\frac{-1}{6}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
9. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{3}{2} - (\frac{-5}{3}) }= a^{\frac{19}{6}}\\=\sqrt[6]{ a^{19} }=|a^{3}|.\sqrt[6]{ a }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{2} - \frac{2}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{3}{4}}}{a^{1}}\\= a^{ \frac{3}{4} - 1 }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
12. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{3} - (\frac{-5}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)