Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{4}{5}}}{y^{1}}\\= y^{ \frac{4}{5} - 1 }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
4. \(\dfrac{y^{-1}}{y^{\frac{4}{5}}}\\= y^{ -1 - \frac{4}{5} }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{1}{2} - (\frac{-1}{5}) }= q^{\frac{7}{10}}\\=\sqrt[10]{ q^{7} }\\---------------\)
6. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{1}{5}}}\\= y^{ \frac{1}{4} - \frac{1}{5} }= y^{\frac{1}{20}}\\=\sqrt[20]{ y }\\---------------\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{-1}}\\= y^{ \frac{-1}{2} - (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\dfrac{q^{\frac{-1}{5}}}{q^{1}}\\= q^{ \frac{-1}{5} - 1 }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
9. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{4}{3} - (\frac{-5}{4}) }= q^{\frac{31}{12}}\\=\sqrt[12]{ q^{31} }=|q^{2}|.\sqrt[12]{ q^{7} }\\---------------\)
10. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{2}{3} - \frac{1}{4} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
11. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
12. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)