Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{2}{3}}}\\= y^{ 1 - \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
3. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-4}{5} - \frac{1}{6} }= y^{\frac{-29}{30}}\\=\frac{1}{\sqrt[30]{ y^{29} }}=\frac{1}{\sqrt[30]{ y^{29} }}. \color{purple}{\frac{\sqrt[30]{ y }}{\sqrt[30]{ y }}} \\=\frac{\sqrt[30]{ y }}{|y|}\\---------------\)
4. \(\dfrac{a^{\frac{-5}{4}}}{a^{1}}\\= a^{ \frac{-5}{4} - 1 }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
5. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
6. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{2} - (\frac{-1}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-1}{5} - \frac{5}{4} }= y^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ y^{29} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{9} }}=\frac{1}{|y|.\sqrt[20]{ y^{9} }} \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{5}{6}}}\\= y^{ \frac{5}{6} - \frac{5}{6} }= y^{0}\\=1\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{1}{3}}}\\= x^{ -1 - \frac{1}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{1}{5}}}\\= y^{ -1 - \frac{1}{5} }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{-4}{3}}}{y^{-1}}\\= y^{ \frac{-4}{3} - (-1) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)