Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{1}{3}}}\\= y^{ 1 - \frac{1}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
2. \(\dfrac{a^{-2}}{a^{\frac{-2}{5}}}\\= a^{ -2 - (\frac{-2}{5}) }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{2} - \frac{2}{3} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{-2}{5}}}{x^{2}}\\= x^{ \frac{-2}{5} - 2 }= x^{\frac{-12}{5}}\\=\frac{1}{\sqrt[5]{ x^{12} }}\\=\frac{1}{x^{2}.\sqrt[5]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{3}}\\---------------\)
5. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-3}{4} - \frac{2}{3} }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{3}{4} - (\frac{-1}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{6}}}{x^{2}}\\= x^{ \frac{-1}{6} - 2 }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{-2}}\\= y^{ \frac{-1}{2} - (-2) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
9. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{2}{3} - \frac{5}{6} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{6} - \frac{2}{3} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-3}{5}}}{a^{-1}}\\= a^{ \frac{-3}{5} - (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
12. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-2}{3} - \frac{2}{5} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)