Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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