Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{4} - \frac{1}{3} }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{4} - \frac{2}{5} }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-5}{2} - \frac{5}{3} }= x^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ x^{25} }}\\=\frac{1}{|x^{4}|.\sqrt[6]{ x }}=\frac{1}{|x^{4}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{5}|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{1}{2} - \frac{4}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{1}}\\= q^{ \frac{1}{3} - 1 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
6. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{2}{5} - \frac{3}{2} }= y^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[10]{ y }}=\frac{1}{|y|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
9. \(\dfrac{y^{2}}{y^{\frac{-5}{3}}}\\= y^{ 2 - (\frac{-5}{3}) }= y^{\frac{11}{3}}\\=\sqrt[3]{ y^{11} }=y^{3}.\sqrt[3]{ y^{2} }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{2} - \frac{3}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{4}{5} - (\frac{-5}{6}) }= y^{\frac{49}{30}}\\=\sqrt[30]{ y^{49} }=|y|.\sqrt[30]{ y^{19} }\\---------------\)
12. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-3}{4} - (\frac{-5}{4}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)