Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
2. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{3}{2} - (\frac{-1}{6}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{5}{6} - (\frac{-3}{2}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{4}{3} - (\frac{-1}{4}) }= q^{\frac{19}{12}}\\=\sqrt[12]{ q^{19} }=|q|.\sqrt[12]{ q^{7} }\\---------------\)
5. \(\dfrac{q^{\frac{-5}{4}}}{q^{-1}}\\= q^{ \frac{-5}{4} - (-1) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
6. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{2}{5} - (\frac{-5}{6}) }= x^{\frac{37}{30}}\\=\sqrt[30]{ x^{37} }=|x|.\sqrt[30]{ x^{7} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-1}{6} - \frac{4}{3} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{5} - (\frac{-1}{3}) }= q^{\frac{8}{15}}\\=\sqrt[15]{ q^{8} }\\---------------\)
9. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{6} - \frac{1}{3} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{1}{2} - (\frac{-1}{4}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
11. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-3}{5} - \frac{1}{3} }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{1}{2} - (\frac{-5}{2}) }= a^{3}\\\\---------------\)