Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{3}{2} - (\frac{-4}{3}) }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)
2. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{5}{2} - (\frac{-5}{4}) }= x^{\frac{15}{4}}\\=\sqrt[4]{ x^{15} }=|x^{3}|.\sqrt[4]{ x^{3} }\\---------------\)
3. \(\dfrac{a^{\frac{-2}{3}}}{a^{-1}}\\= a^{ \frac{-2}{3} - (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
4. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-3}{5} - \frac{3}{4} }= x^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ x^{27} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{7} }}=\frac{1}{|x|.\sqrt[20]{ x^{7} }} \color{purple}{\frac{\sqrt[20]{ x^{13} }}{\sqrt[20]{ x^{13} }}} \\=\frac{\sqrt[20]{ x^{13} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{1}{3} - (\frac{-2}{5}) }= q^{\frac{11}{15}}\\=\sqrt[15]{ q^{11} }\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{3}{5}}}\\= q^{ -1 - \frac{3}{5} }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{4}{3} - (\frac{-1}{4}) }= q^{\frac{19}{12}}\\=\sqrt[12]{ q^{19} }=|q|.\sqrt[12]{ q^{7} }\\---------------\)
8. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{5} - (\frac{-5}{4}) }= x^{\frac{29}{20}}\\=\sqrt[20]{ x^{29} }=|x|.\sqrt[20]{ x^{9} }\\---------------\)
9. \(\dfrac{a^{-2}}{a^{\frac{2}{3}}}\\= a^{ -2 - \frac{2}{3} }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
10. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-4}{5} - \frac{1}{2} }= q^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{3} }}=\frac{1}{|q|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{4} - \frac{4}{5} }= x^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ x^{21} }}\\=\frac{1}{|x|.\sqrt[20]{ x }}=\frac{1}{|x|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{1}{5}}}{q^{-1}}\\= q^{ \frac{1}{5} - (-1) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)