Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{-1}{2}}}\\= y^{ 1 - (\frac{-1}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-5}{3} - (\frac{-3}{5}) }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{1}{4}}}{a^{1}}\\= a^{ \frac{1}{4} - 1 }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
4. \(\dfrac{a^{\frac{4}{5}}}{a^{1}}\\= a^{ \frac{4}{5} - 1 }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
5. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{6} - \frac{1}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{-3}{4}}}{a^{-1}}\\= a^{ \frac{-3}{4} - (-1) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-5}{2} - (\frac{-3}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
8. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{5}{3} - (\frac{-5}{6}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
9. \(\dfrac{x^{2}}{x^{1}}\\= x^{ 2 - 1 }= x^{1}\\\\---------------\)
10. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-1}{4} - (\frac{-5}{6}) }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)
11. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-3}{2} - (\frac{-4}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{4}}}\\= q^{ \frac{1}{2} - \frac{1}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)