Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-1}{5} - (\frac{-3}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
2. \(\dfrac{x^{-2}}{x^{\frac{-1}{3}}}\\= x^{ -2 - (\frac{-1}{3}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{-3}{5}}}{a^{1}}\\= a^{ \frac{-3}{5} - 1 }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{2}}\\= y^{ \frac{-2}{3} - 2 }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
5. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{1}{5} - (\frac{-5}{3}) }= q^{\frac{28}{15}}\\=\sqrt[15]{ q^{28} }=q.\sqrt[15]{ q^{13} }\\---------------\)
6. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
7. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-5}{2} - (\frac{-1}{5}) }= q^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ q^{23} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{3}|}\\---------------\)
8. \(\dfrac{a^{-1}}{a^{\frac{-5}{3}}}\\= a^{ -1 - (\frac{-5}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{-2}}\\= x^{ \frac{-1}{2} - (-2) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{3}{5}}}\\= x^{ -1 - \frac{3}{5} }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{5} - (\frac{-3}{4}) }= a^{\frac{19}{20}}\\=\sqrt[20]{ a^{19} }\\---------------\)
12. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-2}{3} - \frac{5}{6} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)