Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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