Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{2} - (\frac{-1}{2}) }= x^{1}\\\\---------------\)
2. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{6} - (\frac{-1}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
3. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{3}{4} - (\frac{-1}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
4. \(\dfrac{y^{\frac{-2}{5}}}{y^{-1}}\\= y^{ \frac{-2}{5} - (-1) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{6}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
6. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-4}{5} - \frac{5}{2} }= a^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ a^{33} }}\\=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{4}|}\\---------------\)
7. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{3} - \frac{1}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
8. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{5} - \frac{2}{3} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
9. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-4}{3} - (\frac{-3}{4}) }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{3}}}{q^{-1}}\\= q^{ \frac{-1}{3} - (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
11. \(\dfrac{y^{\frac{5}{4}}}{y^{2}}\\= y^{ \frac{5}{4} - 2 }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-2}{3} - \frac{2}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)