Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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