Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{6} - \frac{2}{5} }= q^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ q^{7} }}=\frac{1}{\sqrt[30]{ q^{7} }}. \color{purple}{\frac{\sqrt[30]{ q^{23} }}{\sqrt[30]{ q^{23} }}} \\=\frac{\sqrt[30]{ q^{23} }}{|q|}\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{2} - (\frac{-3}{4}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
3. \(\dfrac{a^{1}}{a^{-2}}\\= a^{ 1 - (-2) }= a^{3}\\\\---------------\)
4. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{5}{3}}}\\= x^{ \frac{3}{5} - \frac{5}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{-5}{6}}}{q^{-2}}\\= q^{ \frac{-5}{6} - (-2) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{2}{5}}}{a^{1}}\\= a^{ \frac{2}{5} - 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{4}{5}}}\\= a^{ \frac{2}{5} - \frac{4}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
11. \(\dfrac{x^{-2}}{x^{1}}\\= x^{ -2 - 1 }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
12. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{1}{6} - (\frac{-5}{6}) }= q^{1}\\\\---------------\)