Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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