Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{-1}{6}}}\\= y^{ -1 - (\frac{-1}{6}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{3} - \frac{1}{2} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{1}{3}}}\\= q^{ -1 - \frac{1}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
4. \(\dfrac{x^{\frac{4}{3}}}{x^{-1}}\\= x^{ \frac{4}{3} - (-1) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{2} - \frac{2}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{5}{2}}}\\= x^{ \frac{3}{4} - \frac{5}{2} }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-2}{3}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
8. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{1}{3} - (\frac{-4}{5}) }= x^{\frac{17}{15}}\\=\sqrt[15]{ x^{17} }=x.\sqrt[15]{ x^{2} }\\---------------\)
9. \(\dfrac{q^{2}}{q^{\frac{-1}{5}}}\\= q^{ 2 - (\frac{-1}{5}) }= q^{\frac{11}{5}}\\=\sqrt[5]{ q^{11} }=q^{2}.\sqrt[5]{ q }\\---------------\)
10. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-2}{3} - \frac{1}{5} }= q^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ q^{13} }}=\frac{1}{\sqrt[15]{ q^{13} }}. \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q}\\---------------\)
11. \(\dfrac{y^{\frac{-2}{5}}}{y^{2}}\\= y^{ \frac{-2}{5} - 2 }= y^{\frac{-12}{5}}\\=\frac{1}{\sqrt[5]{ y^{12} }}\\=\frac{1}{y^{2}.\sqrt[5]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{3}}\\---------------\)
12. \(\dfrac{a^{\frac{-5}{4}}}{a^{-1}}\\= a^{ \frac{-5}{4} - (-1) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)