Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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