Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
2. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{6} - \frac{1}{2} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
4. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{1}{5} - (\frac{-4}{5}) }= y^{1}\\\\---------------\)
5. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{1}{6} - (\frac{-1}{5}) }= y^{\frac{11}{30}}\\=\sqrt[30]{ y^{11} }\\---------------\)
6. \(\dfrac{q^{1}}{q^{2}}\\= q^{ 1 - 2 }= q^{-1}\\=\frac{1}{q}\\---------------\)
7. \(\dfrac{x^{\frac{-3}{5}}}{x^{1}}\\= x^{ \frac{-3}{5} - 1 }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{2} - \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{1}{5} - (\frac{-3}{4}) }= x^{\frac{19}{20}}\\=\sqrt[20]{ x^{19} }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{4}}}{q^{1}}\\= q^{ \frac{-1}{4} - 1 }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-1}{2}}}\\= x^{ 1 - (\frac{-1}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
12. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-3}{2} - (\frac{-4}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)