Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{5}{6}}}\\= x^{ -1 - \frac{5}{6} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{2}{3}}}\\= q^{ -1 - \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{3}{2} - \frac{5}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{2}{5} - (\frac{-2}{5}) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{1}{4}}}\\= x^{ -1 - \frac{1}{4} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{3}{5} - (\frac{-4}{3}) }= y^{\frac{29}{15}}\\=\sqrt[15]{ y^{29} }=y.\sqrt[15]{ y^{14} }\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{1}{3} - \frac{1}{4} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
8. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{1}{3} - (\frac{-5}{2}) }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{2}{5}}}\\= x^{ -1 - \frac{2}{5} }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{-1}{6}}}\\= y^{ 1 - (\frac{-1}{6}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
11. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-2}{3} - \frac{1}{2} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{4}{5} - (\frac{-2}{5}) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)