Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{3}}}{a^{1}}\\= a^{ \frac{1}{3} - 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
2. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{1}{4} - (\frac{-5}{2}) }= x^{\frac{11}{4}}\\=\sqrt[4]{ x^{11} }=|x^{2}|.\sqrt[4]{ x^{3} }\\---------------\)
3. \(\dfrac{x^{-2}}{x^{\frac{-1}{3}}}\\= x^{ -2 - (\frac{-1}{3}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
4. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{3}{5} - (\frac{-5}{6}) }= x^{\frac{43}{30}}\\=\sqrt[30]{ x^{43} }=|x|.\sqrt[30]{ x^{13} }\\---------------\)
5. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{3}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{5}{6} - (\frac{-2}{5}) }= q^{\frac{37}{30}}\\=\sqrt[30]{ q^{37} }=|q|.\sqrt[30]{ q^{7} }\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
8. \(\dfrac{q^{2}}{q^{\frac{-1}{2}}}\\= q^{ 2 - (\frac{-1}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
9. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-2}{3} - (\frac{-5}{6}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
10. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{1}{3} - \frac{1}{4} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
11. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-2}{3} - (\frac{-2}{3}) }= a^{0}\\=1\\---------------\)
12. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-2}{3} - (\frac{-3}{5}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)