Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{5}{3} - (\frac{-2}{5}) }= y^{\frac{31}{15}}\\=\sqrt[15]{ y^{31} }=y^{2}.\sqrt[15]{ y }\\---------------\)
2. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{2}{5} - (\frac{-1}{3}) }= y^{\frac{11}{15}}\\=\sqrt[15]{ y^{11} }\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{3}{4}}}\\= a^{ -1 - \frac{3}{4} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{3}{4} - (\frac{-1}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-4}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{3} - \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
7. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\dfrac{y^{\frac{5}{3}}}{y^{-1}}\\= y^{ \frac{5}{3} - (-1) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{1}{6}}}\\= q^{ 1 - \frac{1}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{5}{4} - (\frac{-5}{2}) }= x^{\frac{15}{4}}\\=\sqrt[4]{ x^{15} }=|x^{3}|.\sqrt[4]{ x^{3} }\\---------------\)
11. \(\dfrac{q^{\frac{1}{5}}}{q^{1}}\\= q^{ \frac{1}{5} - 1 }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
12. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{2}{3} - (\frac{-5}{6}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)