Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{2}{5}}}\\= x^{ \frac{2}{5} - \frac{2}{5} }= x^{0}\\=1\\---------------\)
2. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{3}{5} - (\frac{-2}{5}) }= q^{1}\\\\---------------\)
3. \(\dfrac{q^{\frac{-5}{6}}}{q^{-1}}\\= q^{ \frac{-5}{6} - (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{4}{3} - \frac{5}{6} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
5. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{2}{3} - \frac{1}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
6. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-3}{5} - \frac{2}{3} }= x^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ x^{19} }}\\=\frac{1}{x.\sqrt[15]{ x^{4} }}=\frac{1}{x.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{4} - \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
8. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{4}}}\\= a^{ \frac{2}{3} - \frac{1}{4} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
9. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{5}{3} - (\frac{-3}{2}) }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-2}{3}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
11. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{4}{5} - (\frac{-3}{4}) }= x^{\frac{31}{20}}\\=\sqrt[20]{ x^{31} }=|x|.\sqrt[20]{ x^{11} }\\---------------\)
12. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{2} - (\frac{-2}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)