Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-3}{5} - \frac{2}{3} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)
2. \(\dfrac{a^{\frac{-2}{3}}}{a^{-1}}\\= a^{ \frac{-2}{3} - (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{q^{1}}{q^{\frac{-3}{5}}}\\= q^{ 1 - (\frac{-3}{5}) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{2} - (\frac{-5}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
6. \(\dfrac{x^{-2}}{x^{\frac{2}{3}}}\\= x^{ -2 - \frac{2}{3} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{-1}}\\= q^{ \frac{1}{3} - (-1) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
8. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-4}{3} - \frac{1}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{2} - \frac{4}{5} }= x^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{3} }}=\frac{1}{|x|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{2}{3} - (\frac{-1}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{2} - \frac{1}{2} }= q^{1}\\\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{2}{3}}}\\= y^{ 1 - \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)