Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-3}{4} - \frac{3}{2} }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{2}{3} - (\frac{-1}{6}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-1}{5} - \frac{5}{3} }= y^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ y^{28} }}\\=\frac{1}{y.\sqrt[15]{ y^{13} }}=\frac{1}{y.\sqrt[15]{ y^{13} }} \color{purple}{\frac{\sqrt[15]{ y^{2} }}{\sqrt[15]{ y^{2} }}} \\=\frac{\sqrt[15]{ y^{2} }}{y^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{3}) }= y^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ y^{7} }}=\frac{1}{\sqrt[15]{ y^{7} }}. \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y}\\---------------\)
5. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{4} - \frac{1}{3} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{3} - \frac{1}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{2}{5} - (\frac{-3}{2}) }= y^{\frac{19}{10}}\\=\sqrt[10]{ y^{19} }=|y|.\sqrt[10]{ y^{9} }\\---------------\)
8. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{5}{2}}}\\= x^{ \frac{5}{4} - \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{1}{4}}}{a^{1}}\\= a^{ \frac{1}{4} - 1 }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
10. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-5}{3} - (\frac{-2}{3}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
11. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-5}{3} - \frac{4}{3} }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
12. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-3}{2} - (\frac{-5}{6}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)