Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{3} - \frac{1}{2} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{2}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
3. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{5}{2} - \frac{2}{5} }= y^{\frac{21}{10}}\\=\sqrt[10]{ y^{21} }=|y^{2}|.\sqrt[10]{ y }\\---------------\)
4. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
5. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{1}{4} - (\frac{-2}{3}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
8. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-4}{5} - (\frac{-3}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
9. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{5}{2} - \frac{3}{5} }= y^{\frac{19}{10}}\\=\sqrt[10]{ y^{19} }=|y|.\sqrt[10]{ y^{9} }\\---------------\)
10. \(\dfrac{q^{-2}}{q^{-1}}\\= q^{ -2 - (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{2}}\\= q^{ \frac{-1}{2} - 2 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
12. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-3}{4} - (\frac{-1}{3}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)