Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{2} - \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
2. \(\dfrac{a^{\frac{1}{6}}}{a^{-1}}\\= a^{ \frac{1}{6} - (-1) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{1}{6}}}\\= y^{ -1 - \frac{1}{6} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{3} - \frac{1}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
5. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-5}{3} - \frac{1}{6} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{2} - (\frac{-1}{2}) }= a^{1}\\\\---------------\)
7. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-1}{3} - \frac{4}{5} }= y^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ y^{17} }}\\=\frac{1}{y.\sqrt[15]{ y^{2} }}=\frac{1}{y.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{5}{4}}}{x^{-1}}\\= x^{ \frac{5}{4} - (-1) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
9. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-5}{2} - (\frac{-2}{5}) }= y^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ y^{21} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y }}=\frac{1}{|y^{2}|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{3}|}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{2}{3} - \frac{3}{4} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
11. \(\dfrac{y^{1}}{y^{\frac{2}{3}}}\\= y^{ 1 - \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
12. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)