Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{3}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
2. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-5}{2} - (\frac{-4}{3}) }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{3}{4} - (\frac{-5}{6}) }= q^{\frac{19}{12}}\\=\sqrt[12]{ q^{19} }=|q|.\sqrt[12]{ q^{7} }\\---------------\)
4. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{4}{3} - \frac{5}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{2} - \frac{1}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{4} - \frac{2}{3} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
7. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-5}{3} - (\frac{-1}{4}) }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
9. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-2}{3} - (\frac{-4}{5}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
10. \(\dfrac{y^{\frac{2}{5}}}{y^{1}}\\= y^{ \frac{2}{5} - 1 }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{-1}}\\= q^{ \frac{-1}{2} - (-1) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)