Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{-1}{4}}}\\= q^{ 1 - (\frac{-1}{4}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{-3}{4}}}\\= q^{ 1 - (\frac{-3}{4}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
3. \(\dfrac{q^{\frac{2}{3}}}{q^{-1}}\\= q^{ \frac{2}{3} - (-1) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-5}{3} - \frac{1}{2} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{4}{5} - (\frac{-1}{5}) }= q^{1}\\\\---------------\)
7. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{5}{2} - (\frac{-3}{5}) }= x^{\frac{31}{10}}\\=\sqrt[10]{ x^{31} }=|x^{3}|.\sqrt[10]{ x }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{2}) }= x^{2}\\\\---------------\)
9. \(\dfrac{x^{\frac{1}{4}}}{x^{-1}}\\= x^{ \frac{1}{4} - (-1) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-1}{5} - (\frac{-1}{4}) }= q^{\frac{1}{20}}\\=\sqrt[20]{ q }\\---------------\)
11. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-2}{3} - \frac{1}{6} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
12. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-5}{3} - (\frac{-5}{6}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)