Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{1}{3} - (\frac{-3}{5}) }= a^{\frac{14}{15}}\\=\sqrt[15]{ a^{14} }\\---------------\)
2. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{3} - (\frac{-1}{6}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
3. \(\dfrac{x^{\frac{4}{5}}}{x^{-1}}\\= x^{ \frac{4}{5} - (-1) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
4. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{6} - \frac{1}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{2}{3} - \frac{4}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{-1}{2}}}\\= a^{ -1 - (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\dfrac{q^{\frac{-3}{2}}}{q^{-1}}\\= q^{ \frac{-3}{2} - (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{6}}}{a^{-1}}\\= a^{ \frac{-1}{6} - (-1) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
9. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-2}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{2}{3} - \frac{1}{4} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
11. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-3}{5} - \frac{5}{4} }= y^{\frac{-37}{20}}\\=\frac{1}{\sqrt[20]{ y^{37} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{17} }}=\frac{1}{|y|.\sqrt[20]{ y^{17} }} \color{purple}{\frac{\sqrt[20]{ y^{3} }}{\sqrt[20]{ y^{3} }}} \\=\frac{\sqrt[20]{ y^{3} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{3} - \frac{1}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)