Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{6}}}{y^{1}}\\= y^{ \frac{1}{6} - 1 }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{2}}\\= y^{ \frac{2}{3} - 2 }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{2}) }= q^{0}\\=1\\---------------\)
4. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-3}{4} - \frac{1}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{2}{3}}}\\= x^{ \frac{5}{6} - \frac{2}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{2} - \frac{4}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
7. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-5}{3} - (\frac{-2}{5}) }= x^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ x^{19} }}\\=\frac{1}{x.\sqrt[15]{ x^{4} }}=\frac{1}{x.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{2}}\\---------------\)
8. \(\dfrac{y^{\frac{3}{2}}}{y^{1}}\\= y^{ \frac{3}{2} - 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{4}{5} - (\frac{-4}{3}) }= a^{\frac{32}{15}}\\=\sqrt[15]{ a^{32} }=a^{2}.\sqrt[15]{ a^{2} }\\---------------\)
10. \(\dfrac{q^{\frac{3}{5}}}{q^{1}}\\= q^{ \frac{3}{5} - 1 }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
11. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{4}{3} - (\frac{-2}{3}) }= a^{2}\\\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{-1}}\\= a^{ \frac{-1}{2} - (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)