Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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