Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{5} - \frac{5}{6} }= a^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ a^{31} }}\\=\frac{1}{|a|.\sqrt[30]{ a }}=\frac{1}{|a|.\sqrt[30]{ a }} \color{purple}{\frac{\sqrt[30]{ a^{29} }}{\sqrt[30]{ a^{29} }}} \\=\frac{\sqrt[30]{ a^{29} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{6}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
3. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{4}{5} - (\frac{-5}{3}) }= y^{\frac{37}{15}}\\=\sqrt[15]{ y^{37} }=y^{2}.\sqrt[15]{ y^{7} }\\---------------\)
4. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{4}{5} - (\frac{-5}{6}) }= a^{\frac{49}{30}}\\=\sqrt[30]{ a^{49} }=|a|.\sqrt[30]{ a^{19} }\\---------------\)
5. \(\dfrac{x^{1}}{x^{\frac{-2}{3}}}\\= x^{ 1 - (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
6. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
7. \(\dfrac{a^{\frac{1}{6}}}{a^{-2}}\\= a^{ \frac{1}{6} - (-2) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{5}}}{x^{1}}\\= x^{ \frac{-1}{5} - 1 }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{4}{5} - (\frac{-2}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
10. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{1}{4} - \frac{3}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{-2}{5}}}{y^{1}}\\= y^{ \frac{-2}{5} - 1 }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{2} - \frac{2}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)