Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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