Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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