Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-5}{6} - \frac{3}{2} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{1}}\\= a^{ \frac{2}{3} - 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
3. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{2}{3} - (\frac{-2}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
4. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{2}{3} - (\frac{-3}{4}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
5. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{1}{3} - \frac{1}{4} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
7. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{3}{4} - (\frac{-1}{3}) }= a^{\frac{13}{12}}\\=\sqrt[12]{ a^{13} }=|a|.\sqrt[12]{ a }\\---------------\)
8. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{1}{5} - \frac{5}{3} }= a^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ a^{22} }}\\=\frac{1}{a.\sqrt[15]{ a^{7} }}=\frac{1}{a.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{1}{5} - (\frac{-5}{6}) }= x^{\frac{31}{30}}\\=\sqrt[30]{ x^{31} }=|x|.\sqrt[30]{ x }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-1}{3} - \frac{3}{2} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{-2}{5}}}{x^{1}}\\= x^{ \frac{-2}{5} - 1 }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{5}{6}}}{q^{-2}}\\= q^{ \frac{5}{6} - (-2) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)