Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{4}{5}}}{x^{-1}}\\= x^{ \frac{4}{5} - (-1) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
2. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{2} - \frac{1}{5} }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{5} - (\frac{-3}{2}) }= y^{\frac{13}{10}}\\=\sqrt[10]{ y^{13} }=|y|.\sqrt[10]{ y^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{4}{5} - (\frac{-1}{2}) }= x^{\frac{13}{10}}\\=\sqrt[10]{ x^{13} }=|x|.\sqrt[10]{ x^{3} }\\---------------\)
7. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{5}{2} - \frac{1}{5} }= y^{\frac{23}{10}}\\=\sqrt[10]{ y^{23} }=|y^{2}|.\sqrt[10]{ y^{3} }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{3} - \frac{1}{2} }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{4} - \frac{2}{3} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{5}{2}}}\\= y^{ -1 - \frac{5}{2} }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)