Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{1}{6} - (\frac{-2}{5}) }= a^{\frac{17}{30}}\\=\sqrt[30]{ a^{17} }\\---------------\)
2. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{5}{2} - \frac{5}{6} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{3}{4}}}{y^{-1}}\\= y^{ \frac{3}{4} - (-1) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
4. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-5}{2} - \frac{5}{2} }= a^{-5}\\=\frac{1}{a^{5}}\\---------------\)
5. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-1}{2} - \frac{5}{6} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{-4}{5}}}\\= a^{ -1 - (\frac{-4}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
7. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
8. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{4}{3} - (\frac{-1}{2}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
9. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{3}{4} - (\frac{-5}{4}) }= x^{2}\\\\---------------\)
10. \(\dfrac{y^{\frac{-4}{5}}}{y^{-2}}\\= y^{ \frac{-4}{5} - (-2) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{4}{3}}}\\= a^{ 1 - \frac{4}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
12. \(\dfrac{x^{\frac{5}{2}}}{x^{-1}}\\= x^{ \frac{5}{2} - (-1) }= x^{\frac{7}{2}}\\= \sqrt{ x^{7} } =|x^{3}|. \sqrt{ x } \\---------------\)