Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{3}{5} - (\frac{-1}{3}) }= y^{\frac{14}{15}}\\=\sqrt[15]{ y^{14} }\\---------------\)
2. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-5}{4} - \frac{4}{5} }= q^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ q^{41} }}\\=\frac{1}{|q^{2}|.\sqrt[20]{ q }}=\frac{1}{|q^{2}|.\sqrt[20]{ q }} \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q^{3}|}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{5}{6}}}\\= a^{ 1 - \frac{5}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
4. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{2}{3} - (\frac{-5}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{a^{\frac{-2}{5}}}{a^{-1}}\\= a^{ \frac{-2}{5} - (-1) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{5}{4}}}\\= x^{ \frac{1}{6} - \frac{5}{4} }= x^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[12]{ x }}=\frac{1}{|x|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{3}{4}}}\\= a^{ 1 - \frac{3}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
9. \(\dfrac{a^{\frac{1}{3}}}{a^{-2}}\\= a^{ \frac{1}{3} - (-2) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-1}{2} - \frac{1}{6} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-2}{5}}}\\= x^{ 1 - (\frac{-2}{5}) }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
12. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{4}{3} - \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)