Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-2}}{x^{\frac{2}{5}}}\\= x^{ -2 - \frac{2}{5} }= x^{\frac{-12}{5}}\\=\frac{1}{\sqrt[5]{ x^{12} }}\\=\frac{1}{x^{2}.\sqrt[5]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{3}}\\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{6}}}\\= x^{ \frac{2}{3} - \frac{1}{6} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
3. \(\dfrac{q^{1}}{q^{\frac{1}{6}}}\\= q^{ 1 - \frac{1}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
4. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{5} - (\frac{-1}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{1}{2} - \frac{2}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{3} - \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
8. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{3}{4} - \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
9. \(\dfrac{y^{\frac{3}{5}}}{y^{1}}\\= y^{ \frac{3}{5} - 1 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{2}{3} - \frac{3}{4} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
11. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{4}{5} - (\frac{-5}{4}) }= a^{\frac{41}{20}}\\=\sqrt[20]{ a^{41} }=|a^{2}|.\sqrt[20]{ a }\\---------------\)