Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{2}) }= a^{1}\\\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\dfrac{q^{\frac{5}{3}}}{q^{1}}\\= q^{ \frac{5}{3} - 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-5}{6} - (\frac{-2}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
5. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{5}{3} - \frac{2}{3} }= a^{1}\\\\---------------\)
6. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{4}{3} - \frac{5}{6} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
7. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-3}{2} - \frac{5}{4} }= y^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ y^{11} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y^{3} }}=\frac{1}{|y^{2}|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{3}|}\\---------------\)
8. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-4}{5} - \frac{5}{2} }= x^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ x^{33} }}\\=\frac{1}{|x^{3}|.\sqrt[10]{ x^{3} }}=\frac{1}{|x^{3}|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{4}|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
10. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-5}{3} - \frac{5}{2} }= a^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ a^{25} }}\\=\frac{1}{|a^{4}|.\sqrt[6]{ a }}=\frac{1}{|a^{4}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{5}|}\\---------------\)
11. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
12. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-3}{4} - \frac{1}{6} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)