Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{\frac{2}{3}}}\\= a^{ -1 - \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{4}{3}}}\\= q^{ -1 - \frac{4}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
3. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{3}{5} - (\frac{-5}{3}) }= q^{\frac{34}{15}}\\=\sqrt[15]{ q^{34} }=q^{2}.\sqrt[15]{ q^{4} }\\---------------\)
4. \(\dfrac{q^{-2}}{q^{\frac{5}{3}}}\\= q^{ -2 - \frac{5}{3} }= q^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ q^{11} }}\\=\frac{1}{q^{3}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{3}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{4}}\\---------------\)
5. \(\dfrac{x^{\frac{-4}{5}}}{x^{-1}}\\= x^{ \frac{-4}{5} - (-1) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{1}{3} - (\frac{-5}{3}) }= a^{2}\\\\---------------\)
7. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-3}{2} - (\frac{-2}{3}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
8. \(\dfrac{x^{\frac{3}{4}}}{x^{-2}}\\= x^{ \frac{3}{4} - (-2) }= x^{\frac{11}{4}}\\=\sqrt[4]{ x^{11} }=|x^{2}|.\sqrt[4]{ x^{3} }\\---------------\)
9. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{3}{2} - \frac{1}{3} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{3} - \frac{1}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{2} - \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
12. \(\dfrac{x^{1}}{x^{\frac{-5}{3}}}\\= x^{ 1 - (\frac{-5}{3}) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)