Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-5}{4} - \frac{2}{3} }= x^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ x^{23} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{11} }}=\frac{1}{|x|.\sqrt[12]{ x^{11} }} \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-3}{4} - \frac{1}{3} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-2}{5} - (\frac{-1}{3}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
4. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{3} - \frac{1}{2} }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
5. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{5}{3} - \frac{3}{4} }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
6. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-2}{3} - (\frac{-5}{6}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{5}{4} - (\frac{-5}{3}) }= x^{\frac{35}{12}}\\=\sqrt[12]{ x^{35} }=|x^{2}|.\sqrt[12]{ x^{11} }\\---------------\)
8. \(\dfrac{a^{\frac{1}{6}}}{a^{-1}}\\= a^{ \frac{1}{6} - (-1) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-5}{4} - (\frac{-1}{2}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{5}{2}}}\\= y^{ \frac{4}{5} - \frac{5}{2} }= y^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{7} }}=\frac{1}{|y|.\sqrt[10]{ y^{7} }} \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{2}{5} - (\frac{-5}{3}) }= q^{\frac{31}{15}}\\=\sqrt[15]{ q^{31} }=q^{2}.\sqrt[15]{ q }\\---------------\)