Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-4}{5} - \frac{2}{3} }= x^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ x^{22} }}\\=\frac{1}{x.\sqrt[15]{ x^{7} }}=\frac{1}{x.\sqrt[15]{ x^{7} }} \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x^{2}}\\---------------\)
2. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-3}{5} - (\frac{-5}{6}) }= q^{\frac{7}{30}}\\=\sqrt[30]{ q^{7} }\\---------------\)
3. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-3}{4} - \frac{4}{3} }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{4} - \frac{2}{5} }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
5. \(\dfrac{a^{-1}}{a^{2}}\\= a^{ -1 - 2 }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{-2}}\\= a^{ \frac{-2}{3} - (-2) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{6}}}\\= a^{ \frac{1}{2} - \frac{1}{6} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
8. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-5}{4} - \frac{1}{5} }= x^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ x^{29} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{9} }}=\frac{1}{|x|.\sqrt[20]{ x^{9} }} \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{-5}{6}}}\\= a^{ -1 - (\frac{-5}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
10. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-2}{3} - \frac{1}{2} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
12. \(\dfrac{x^{-2}}{x^{\frac{1}{3}}}\\= x^{ -2 - \frac{1}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)