Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{3} - (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
2. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{3}{4} - (\frac{-2}{3}) }= q^{\frac{17}{12}}\\=\sqrt[12]{ q^{17} }=|q|.\sqrt[12]{ q^{5} }\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{2} - \frac{5}{3} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
4. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{1}{2} - (\frac{-4}{3}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{3}{2} - \frac{1}{3} }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{1}{3}}}\\= q^{ 1 - \frac{1}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-3}{5} - (\frac{-1}{2}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
8. \(\dfrac{a^{2}}{a^{\frac{1}{5}}}\\= a^{ 2 - \frac{1}{5} }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
9. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
10. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
11. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-2}{3} - \frac{1}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
12. \(\dfrac{a^{\frac{-3}{2}}}{a^{2}}\\= a^{ \frac{-3}{2} - 2 }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)