Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{5}}}{y^{1}}\\= y^{ \frac{3}{5} - 1 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
2. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{5}{3} - (\frac{-3}{5}) }= a^{\frac{34}{15}}\\=\sqrt[15]{ a^{34} }=a^{2}.\sqrt[15]{ a^{4} }\\---------------\)
3. \(\dfrac{x^{2}}{x^{1}}\\= x^{ 2 - 1 }= x^{1}\\\\---------------\)
4. \(\dfrac{a^{1}}{a^{2}}\\= a^{ 1 - 2 }= a^{-1}\\=\frac{1}{a}\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{2} - \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
6. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-5}{2} - (\frac{-4}{5}) }= y^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{7} }}=\frac{1}{|y|.\sqrt[10]{ y^{7} }} \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-5}{6} - (\frac{-5}{6}) }= a^{0}\\=1\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-5}{6}}}\\= y^{ 1 - (\frac{-5}{6}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{6} - (\frac{-2}{3}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
10. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{1}{6}}}\\= x^{ \frac{5}{2} - \frac{1}{6} }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
11. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{1}{3} - (\frac{-1}{5}) }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
12. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{3}{4}}}\\= a^{ \frac{1}{4} - \frac{3}{4} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)