Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{5} - (\frac{-1}{3}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
2. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{3} - (\frac{-1}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{4}{5}}}\\= q^{ -1 - \frac{4}{5} }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{5}{3}}}\\= q^{ 1 - \frac{5}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
5. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{4}{3} - \frac{1}{3} }= y^{1}\\\\---------------\)
6. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{3} - \frac{3}{2} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{2}{3} - \frac{3}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
8. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{5}{6}}}\\= q^{ \frac{3}{4} - \frac{5}{6} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
9. \(\dfrac{y^{\frac{-3}{4}}}{y^{1}}\\= y^{ \frac{-3}{4} - 1 }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-4}{3} - \frac{5}{4} }= y^{\frac{-31}{12}}\\=\frac{1}{\sqrt[12]{ y^{31} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{3}|}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-5}{6}}}\\= x^{ 1 - (\frac{-5}{6}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
12. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{5} - \frac{2}{3} }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)