Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{6}}}{y^{2}}\\= y^{ \frac{1}{6} - 2 }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
2. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{4} - \frac{2}{3} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{-1}}\\= y^{ \frac{-1}{3} - (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{2}{3} - (\frac{-5}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-1}{5} - \frac{5}{4} }= a^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ a^{29} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{9} }}=\frac{1}{|a|.\sqrt[20]{ a^{9} }} \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{-4}{3}}}{y^{-2}}\\= y^{ \frac{-4}{3} - (-2) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{3}{5} - (\frac{-2}{3}) }= q^{\frac{19}{15}}\\=\sqrt[15]{ q^{19} }=q.\sqrt[15]{ q^{4} }\\---------------\)
8. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{1}{3} - \frac{5}{6} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{4} - \frac{1}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{6}}}{x^{1}}\\= x^{ \frac{-1}{6} - 1 }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
11. \(\dfrac{a^{2}}{a^{\frac{4}{5}}}\\= a^{ 2 - \frac{4}{5} }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{5}{4} - (\frac{-5}{6}) }= y^{\frac{25}{12}}\\=\sqrt[12]{ y^{25} }=|y^{2}|.\sqrt[12]{ y }\\---------------\)