Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{1}{6}}}\\= y^{ -1 - \frac{1}{6} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{-1}}\\= y^{ \frac{-1}{3} - (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{3}{5} - (\frac{-5}{4}) }= a^{\frac{37}{20}}\\=\sqrt[20]{ a^{37} }=|a|.\sqrt[20]{ a^{17} }\\---------------\)
5. \(\dfrac{a^{\frac{2}{3}}}{a^{-1}}\\= a^{ \frac{2}{3} - (-1) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-1}{3} - (\frac{-5}{6}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{3}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
8. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{6} - (\frac{-4}{5}) }= q^{\frac{29}{30}}\\=\sqrt[30]{ q^{29} }\\---------------\)
9. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{2} - (\frac{-2}{3}) }= y^{\frac{19}{6}}\\=\sqrt[6]{ y^{19} }=|y^{3}|.\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{2} - \frac{1}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{3}{2}}}{x^{1}}\\= x^{ \frac{3}{2} - 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{1}{5}}}\\= q^{ \frac{1}{6} - \frac{1}{5} }= q^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ q }}=\frac{1}{\sqrt[30]{ q }}. \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q|}\\---------------\)