Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{5}{4} - (\frac{-3}{5}) }= a^{\frac{37}{20}}\\=\sqrt[20]{ a^{37} }=|a|.\sqrt[20]{ a^{17} }\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{3}{5}}}\\= x^{ -1 - \frac{3}{5} }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{1}{6}}}{a^{-1}}\\= a^{ \frac{1}{6} - (-1) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
4. \(\dfrac{y^{-2}}{y^{1}}\\= y^{ -2 - 1 }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-2}{3} - \frac{1}{2} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-2}{5} - (\frac{-5}{3}) }= y^{\frac{19}{15}}\\=\sqrt[15]{ y^{19} }=y.\sqrt[15]{ y^{4} }\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{1}{3}}}\\= q^{ 1 - \frac{1}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{4}{3}}}{a^{-1}}\\= a^{ \frac{4}{3} - (-1) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
9. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
10. \(\dfrac{q^{\frac{2}{5}}}{q^{-1}}\\= q^{ \frac{2}{5} - (-1) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{1}{3}}}\\= y^{ -1 - \frac{1}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{-2}{3}}}{a^{-1}}\\= a^{ \frac{-2}{3} - (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)