Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-2}{5}}}{x^{1}}\\= x^{ \frac{-2}{5} - 1 }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
2. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{5}{4}}}\\= a^{ \frac{5}{6} - \frac{5}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
3. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{5}{3} - \frac{2}{5} }= x^{\frac{19}{15}}\\=\sqrt[15]{ x^{19} }=x.\sqrt[15]{ x^{4} }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{2}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{5}}}\\= q^{ \frac{5}{4} - \frac{1}{5} }= q^{\frac{21}{20}}\\=\sqrt[20]{ q^{21} }=|q|.\sqrt[20]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{2}{3} - \frac{1}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
7. \(\dfrac{x^{\frac{1}{4}}}{x^{-2}}\\= x^{ \frac{1}{4} - (-2) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{2}}}{a^{1}}\\= a^{ \frac{-5}{2} - 1 }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
9. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{4}{3} - (\frac{-2}{5}) }= a^{\frac{26}{15}}\\=\sqrt[15]{ a^{26} }=a.\sqrt[15]{ a^{11} }\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
11. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-3}{5} - (\frac{-5}{3}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{2} - \frac{2}{5} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)