Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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