Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{2}{3} - \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{2} - (\frac{-1}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
3. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{6} - (\frac{-5}{2}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{4} - (\frac{-5}{2}) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{3} - (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
6. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{3}{4} - (\frac{-3}{5}) }= x^{\frac{27}{20}}\\=\sqrt[20]{ x^{27} }=|x|.\sqrt[20]{ x^{7} }\\---------------\)
7. \(\dfrac{x^{\frac{5}{4}}}{x^{-2}}\\= x^{ \frac{5}{4} - (-2) }= x^{\frac{13}{4}}\\=\sqrt[4]{ x^{13} }=|x^{3}|.\sqrt[4]{ x }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{6}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{5}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
10. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{4} - (\frac{-3}{4}) }= a^{1}\\\\---------------\)
11. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{5}{3} - \frac{4}{5} }= x^{\frac{13}{15}}\\=\sqrt[15]{ x^{13} }\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{-5}{2}}}\\= a^{ -1 - (\frac{-5}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)