Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{4}{3}}}\\= q^{ \frac{2}{5} - \frac{4}{3} }= q^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ q^{14} }}=\frac{1}{\sqrt[15]{ q^{14} }}. \color{purple}{\frac{\sqrt[15]{ q }}{\sqrt[15]{ q }}} \\=\frac{\sqrt[15]{ q }}{q}\\---------------\)
2. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{2} - (\frac{-1}{2}) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{3}{5} - \frac{1}{2} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
4. \(\dfrac{x^{1}}{x^{\frac{-1}{3}}}\\= x^{ 1 - (\frac{-1}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{3}{2} - \frac{3}{5} }= x^{\frac{9}{10}}\\=\sqrt[10]{ x^{9} }\\---------------\)
6. \(\dfrac{a^{\frac{5}{2}}}{a^{-1}}\\= a^{ \frac{5}{2} - (-1) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
7. \(\dfrac{x^{1}}{x^{\frac{4}{3}}}\\= x^{ 1 - \frac{4}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
8. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{4}{3}}}\\= y^{ \frac{4}{5} - \frac{4}{3} }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
9. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{4} - \frac{2}{5} }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
10. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{2}{5} - \frac{5}{6} }= y^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ y^{13} }}=\frac{1}{\sqrt[30]{ y^{13} }}. \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y|}\\---------------\)
11. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{5}{3} - \frac{3}{4} }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
12. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{3} - \frac{5}{2} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)