Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{2}}}{x^{-1}}\\= x^{ \frac{-5}{2} - (-1) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{3}{5}}}\\= a^{ 1 - \frac{3}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{2}{3} - (\frac{-2}{5}) }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
4. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-4}{5} - (\frac{-3}{2}) }= q^{\frac{7}{10}}\\=\sqrt[10]{ q^{7} }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{5}}}{y^{1}}\\= y^{ \frac{-1}{5} - 1 }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{3}{4} - (\frac{-5}{6}) }= q^{\frac{19}{12}}\\=\sqrt[12]{ q^{19} }=|q|.\sqrt[12]{ q^{7} }\\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{-1}}\\= q^{ \frac{2}{3} - (-1) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
8. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{4}{5} - (\frac{-2}{3}) }= q^{\frac{22}{15}}\\=\sqrt[15]{ q^{22} }=q.\sqrt[15]{ q^{7} }\\---------------\)
9. \(\dfrac{a^{\frac{-5}{6}}}{a^{-2}}\\= a^{ \frac{-5}{6} - (-2) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{4} - \frac{1}{4} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
11. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{3} - \frac{1}{2} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{3} - (\frac{-1}{4}) }= a^{\frac{7}{12}}\\=\sqrt[12]{ a^{7} }\\---------------\)