Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{2} - (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-1}{4} - \frac{3}{4} }= a^{-1}\\=\frac{1}{a}\\---------------\)
3. \(\dfrac{x^{2}}{x^{\frac{2}{3}}}\\= x^{ 2 - \frac{2}{3} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
5. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{2}{5} - \frac{2}{3} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
6. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{2}{3}}}\\= y^{ \frac{3}{4} - \frac{2}{3} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
7. \(\dfrac{x^{\frac{4}{5}}}{x^{2}}\\= x^{ \frac{4}{5} - 2 }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{5} - \frac{1}{2} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
9. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-5}{6} - \frac{1}{4} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\\= q^{ \frac{5}{4} - 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
12. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{4} - (\frac{-1}{3}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)