Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{3}}}{q^{2}}\\= q^{ \frac{5}{3} - 2 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{3}{2}}}\\= a^{ -1 - \frac{3}{2} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-1}{6} - (\frac{-1}{5}) }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
4. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{4} - (\frac{-2}{3}) }= y^{\frac{23}{12}}\\=\sqrt[12]{ y^{23} }=|y|.\sqrt[12]{ y^{11} }\\---------------\)
5. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-4}{3} - (\frac{-3}{5}) }= a^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ a^{11} }}=\frac{1}{\sqrt[15]{ a^{11} }}. \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{4} - \frac{1}{5} }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
7. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{3}{2} - (\frac{-2}{3}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{4}{5} - (\frac{-5}{6}) }= y^{\frac{49}{30}}\\=\sqrt[30]{ y^{49} }=|y|.\sqrt[30]{ y^{19} }\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{-5}{6}}}\\= a^{ 1 - (\frac{-5}{6}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{5}{4}}}\\= x^{ 1 - \frac{5}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{3} - \frac{1}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
12. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-2}{3} - \frac{5}{6} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)