Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-2}{3} - \frac{1}{4} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
2. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-4}{5} - (\frac{-5}{3}) }= x^{\frac{13}{15}}\\=\sqrt[15]{ x^{13} }\\---------------\)
3. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-3}{5} - \frac{5}{4} }= q^{\frac{-37}{20}}\\=\frac{1}{\sqrt[20]{ q^{37} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{17} }}=\frac{1}{|q|.\sqrt[20]{ q^{17} }} \color{purple}{\frac{\sqrt[20]{ q^{3} }}{\sqrt[20]{ q^{3} }}} \\=\frac{\sqrt[20]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{2} - \frac{1}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{5}{6} - (\frac{-1}{2}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
7. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{5}{2}}}\\= x^{ \frac{5}{4} - \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{2} - \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-1}{5} - \frac{5}{3} }= y^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ y^{28} }}\\=\frac{1}{y.\sqrt[15]{ y^{13} }}=\frac{1}{y.\sqrt[15]{ y^{13} }} \color{purple}{\frac{\sqrt[15]{ y^{2} }}{\sqrt[15]{ y^{2} }}} \\=\frac{\sqrt[15]{ y^{2} }}{y^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{6} - \frac{1}{4} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{3}{5} - (\frac{-2}{3}) }= x^{\frac{19}{15}}\\=\sqrt[15]{ x^{19} }=x.\sqrt[15]{ x^{4} }\\---------------\)
12. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-5}{2} - (\frac{-5}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)