Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{6}}}\\= a^{ \frac{-1}{4} - \frac{1}{6} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{-3}{2}}}\\= a^{ 1 - (\frac{-3}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
3. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{3}{5} - (\frac{-5}{6}) }= y^{\frac{43}{30}}\\=\sqrt[30]{ y^{43} }=|y|.\sqrt[30]{ y^{13} }\\---------------\)
4. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{3}{5} - (\frac{-1}{6}) }= a^{\frac{23}{30}}\\=\sqrt[30]{ a^{23} }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{3} - \frac{1}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-5}{2} - \frac{1}{3} }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
8. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{2}{3} - \frac{1}{4} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
9. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{5}{3} - (\frac{-1}{5}) }= q^{\frac{28}{15}}\\=\sqrt[15]{ q^{28} }=q.\sqrt[15]{ q^{13} }\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{2}{3} - (\frac{-1}{4}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{2}{5}}}\\= a^{ 1 - \frac{2}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
12. \(\dfrac{y^{\frac{3}{5}}}{y^{1}}\\= y^{ \frac{3}{5} - 1 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)