Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{5}}}{y^{-1}}\\= y^{ \frac{3}{5} - (-1) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{2}{5}}}\\= a^{ -1 - \frac{2}{5} }= a^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ a^{7} }}\\=\frac{1}{a.\sqrt[5]{ a^{2} }}=\frac{1}{a.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{2} - \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{5}{3} - (\frac{-1}{2}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{6} - \frac{3}{2} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{1}{5}}}{x^{-2}}\\= x^{ \frac{1}{5} - (-2) }= x^{\frac{11}{5}}\\=\sqrt[5]{ x^{11} }=x^{2}.\sqrt[5]{ x }\\---------------\)
7. \(\dfrac{y^{-1}}{y^{-2}}\\= y^{ -1 - (-2) }= y^{1}\\\\---------------\)
8. \(\dfrac{y^{\frac{4}{3}}}{y^{1}}\\= y^{ \frac{4}{3} - 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
9. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{1}{4} - (\frac{-5}{3}) }= y^{\frac{23}{12}}\\=\sqrt[12]{ y^{23} }=|y|.\sqrt[12]{ y^{11} }\\---------------\)
10. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-2}{5} - \frac{2}{5} }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
11. \(\dfrac{x^{\frac{1}{3}}}{x^{1}}\\= x^{ \frac{1}{3} - 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{2} - (\frac{-3}{4}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)