Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-3}{2} - \frac{5}{6} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
2. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{4} - \frac{1}{6} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{-2}{5}}}\\= x^{ -1 - (\frac{-2}{5}) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
5. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{1}{6} - (\frac{-4}{5}) }= x^{\frac{29}{30}}\\=\sqrt[30]{ x^{29} }\\---------------\)
6. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\dfrac{x^{1}}{x^{\frac{-3}{2}}}\\= x^{ 1 - (\frac{-3}{2}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{1}{2} - \frac{4}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
9. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{1}{3} - (\frac{-3}{2}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
10. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{2}{3} - \frac{1}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{1}{5}}}\\= x^{ \frac{5}{6} - \frac{1}{5} }= x^{\frac{19}{30}}\\=\sqrt[30]{ x^{19} }\\---------------\)
12. \(\dfrac{y^{\frac{-3}{2}}}{y^{1}}\\= y^{ \frac{-3}{2} - 1 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)