Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-3}{2} - (\frac{-1}{2}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
2. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{3}{5} - \frac{4}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{6} - \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{4}{5}}}\\= a^{ \frac{1}{6} - \frac{4}{5} }= a^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ a^{19} }}=\frac{1}{\sqrt[30]{ a^{19} }}. \color{purple}{\frac{\sqrt[30]{ a^{11} }}{\sqrt[30]{ a^{11} }}} \\=\frac{\sqrt[30]{ a^{11} }}{|a|}\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{5}{6}}}\\= a^{ 1 - \frac{5}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-5}{6} - \frac{3}{5} }= y^{\frac{-43}{30}}\\=\frac{1}{\sqrt[30]{ y^{43} }}\\=\frac{1}{|y|.\sqrt[30]{ y^{13} }}=\frac{1}{|y|.\sqrt[30]{ y^{13} }} \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-3}{4} - (\frac{-5}{3}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
9. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{3} - \frac{2}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
10. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-5}{4} - (\frac{-5}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{5} - (\frac{-5}{6}) }= a^{\frac{19}{30}}\\=\sqrt[30]{ a^{19} }\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{-4}{5}}}\\= x^{ -1 - (\frac{-4}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)