Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{5}{2}}}\\= y^{ -1 - \frac{5}{2} }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{2} - (\frac{-3}{5}) }= y^{\frac{11}{10}}\\=\sqrt[10]{ y^{11} }=|y|.\sqrt[10]{ y }\\---------------\)
3. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{3}{2}}}\\= x^{ \frac{1}{4} - \frac{3}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
4. \(\dfrac{x^{2}}{x^{\frac{1}{3}}}\\= x^{ 2 - \frac{1}{3} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{1}{6}}}{y^{1}}\\= y^{ \frac{1}{6} - 1 }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
6. \(\dfrac{y^{\frac{-2}{5}}}{y^{-1}}\\= y^{ \frac{-2}{5} - (-1) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-5}{2} - \frac{5}{3} }= y^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ y^{25} }}\\=\frac{1}{|y^{4}|.\sqrt[6]{ y }}=\frac{1}{|y^{4}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{5}|}\\---------------\)
8. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{1}{5}}}\\= a^{ \frac{1}{5} - \frac{1}{5} }= a^{0}\\=1\\---------------\)
9. \(\dfrac{y^{-1}}{y^{\frac{1}{5}}}\\= y^{ -1 - \frac{1}{5} }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{4}{5} - (\frac{-2}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
11. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{2} - (\frac{-2}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-5}{2} - (\frac{-1}{4}) }= x^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ x^{9} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x }}=\frac{1}{|x^{2}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{3}|}\\---------------\)