Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{3}}}{q^{-2}}\\= q^{ \frac{1}{3} - (-2) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{y^{-2}}{y^{2}}\\= y^{ -2 - 2 }= y^{-4}\\=\frac{1}{y^{4}}\\---------------\)
3. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{4}{3} - (\frac{-2}{5}) }= q^{\frac{26}{15}}\\=\sqrt[15]{ q^{26} }=q.\sqrt[15]{ q^{11} }\\---------------\)
4. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
5. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-4}{5} - \frac{2}{3} }= x^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ x^{22} }}\\=\frac{1}{x.\sqrt[15]{ x^{7} }}=\frac{1}{x.\sqrt[15]{ x^{7} }} \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x^{2}}\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{5}{3}}}\\= a^{ -1 - \frac{5}{3} }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
7. \(\dfrac{a^{\frac{5}{6}}}{a^{-1}}\\= a^{ \frac{5}{6} - (-1) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
9. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-2}{3} - \frac{3}{2} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
10. \(\dfrac{a^{2}}{a^{-1}}\\= a^{ 2 - (-1) }= a^{3}\\\\---------------\)
11. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
12. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-4}{5} - \frac{1}{2} }= a^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{3} }}=\frac{1}{|a|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{2}|}\\---------------\)