Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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