Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{1}{5} - (\frac{-5}{6}) }= q^{\frac{31}{30}}\\=\sqrt[30]{ q^{31} }=|q|.\sqrt[30]{ q }\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
3. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{2}{3} - (\frac{-3}{2}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
4. \(\dfrac{y^{\frac{2}{3}}}{y^{-1}}\\= y^{ \frac{2}{3} - (-1) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
5. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{3}{4}}}\\= q^{ \frac{3}{5} - \frac{3}{4} }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
6. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
7. \(\dfrac{y^{\frac{-1}{6}}}{y^{-1}}\\= y^{ \frac{-1}{6} - (-1) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
8. \(\dfrac{y^{2}}{y^{1}}\\= y^{ 2 - 1 }= y^{1}\\\\---------------\)
9. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{4}{5} - \frac{1}{2} }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-1}{2} - \frac{2}{5} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
11. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-3}{2} - \frac{1}{4} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-3}{2} - \frac{5}{3} }= x^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ x^{19} }}\\=\frac{1}{|x^{3}|.\sqrt[6]{ x }}=\frac{1}{|x^{3}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{4}|}\\---------------\)