Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{4}{5}}}\\= q^{ \frac{1}{2} - \frac{4}{5} }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
2. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{5}) }= q^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ q^{19} }}=\frac{1}{\sqrt[30]{ q^{19} }}. \color{purple}{\frac{\sqrt[30]{ q^{11} }}{\sqrt[30]{ q^{11} }}} \\=\frac{\sqrt[30]{ q^{11} }}{|q|}\\---------------\)
3. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-5}{2} - (\frac{-3}{4}) }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{2} - \frac{2}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{5} - \frac{2}{3} }= a^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ a^{7} }}=\frac{1}{\sqrt[15]{ a^{7} }}. \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a}\\---------------\)
6. \(\dfrac{x^{2}}{x^{\frac{4}{5}}}\\= x^{ 2 - \frac{4}{5} }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
7. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{5}{3} - \frac{1}{2} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{4} - \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
9. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{2}{3} - (\frac{-2}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{5} - \frac{1}{2} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
11. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-3}{4} - (\frac{-1}{2}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
12. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{4}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)