Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-1}{2} - \frac{3}{2} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
2. \(\dfrac{y^{-2}}{y^{\frac{-4}{5}}}\\= y^{ -2 - (\frac{-4}{5}) }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{1}{4}}}\\= x^{ -1 - \frac{1}{4} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{6}) }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
6. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{3}{5}}}\\= a^{ \frac{1}{6} - \frac{3}{5} }= a^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ a^{13} }}=\frac{1}{\sqrt[30]{ a^{13} }}. \color{purple}{\frac{\sqrt[30]{ a^{17} }}{\sqrt[30]{ a^{17} }}} \\=\frac{\sqrt[30]{ a^{17} }}{|a|}\\---------------\)
7. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-5}{3} - (\frac{-3}{5}) }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{2} - \frac{1}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
9. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{4}{3} - (\frac{-4}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{6} - (\frac{-2}{3}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
11. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{5} - (\frac{-4}{5}) }= q^{1}\\\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{2} - \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)