Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-1}{4} - \frac{3}{2} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{1}{4}}}\\= x^{ -1 - \frac{1}{4} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{2} - \frac{1}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
4. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-5}{6} - (\frac{-3}{5}) }= q^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ q^{7} }}=\frac{1}{\sqrt[30]{ q^{7} }}. \color{purple}{\frac{\sqrt[30]{ q^{23} }}{\sqrt[30]{ q^{23} }}} \\=\frac{\sqrt[30]{ q^{23} }}{|q|}\\---------------\)
5. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{3}{5} - (\frac{-1}{6}) }= x^{\frac{23}{30}}\\=\sqrt[30]{ x^{23} }\\---------------\)
6. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{3}{2} - \frac{2}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
7. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-5}{4} - (\frac{-5}{3}) }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{-2}{5}}}{y^{-1}}\\= y^{ \frac{-2}{5} - (-1) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
9. \(\dfrac{y^{-1}}{y^{\frac{-5}{3}}}\\= y^{ -1 - (\frac{-5}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
11. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{4}}}\\= q^{ \frac{1}{4} - \frac{5}{4} }= q^{-1}\\=\frac{1}{q}\\---------------\)
12. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{5}{6} - (\frac{-1}{3}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)