Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{4} - \frac{2}{3} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
2. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{2}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{-5}{3}}}\\= x^{ -1 - (\frac{-5}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
4. \(\dfrac{a^{2}}{a^{\frac{1}{2}}}\\= a^{ 2 - \frac{1}{2} }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{2}{3} - (\frac{-2}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-2}{5} - \frac{1}{6} }= y^{\frac{-17}{30}}\\=\frac{1}{\sqrt[30]{ y^{17} }}=\frac{1}{\sqrt[30]{ y^{17} }}. \color{purple}{\frac{\sqrt[30]{ y^{13} }}{\sqrt[30]{ y^{13} }}} \\=\frac{\sqrt[30]{ y^{13} }}{|y|}\\---------------\)
7. \(\dfrac{a^{-2}}{a^{\frac{-1}{6}}}\\= a^{ -2 - (\frac{-1}{6}) }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{2}{3}}}{y^{2}}\\= y^{ \frac{2}{3} - 2 }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{2} - (\frac{-1}{2}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
10. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{5}{4} - (\frac{-5}{4}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
11. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{3} - \frac{1}{3} }= q^{0}\\=1\\---------------\)
12. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{1}{6} - (\frac{-5}{6}) }= x^{1}\\\\---------------\)