Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{3}{4} - (\frac{-3}{4}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
2. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-2}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
3. \(\dfrac{y^{\frac{-3}{5}}}{y^{1}}\\= y^{ \frac{-3}{5} - 1 }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-3}{5} - (\frac{-5}{6}) }= a^{\frac{7}{30}}\\=\sqrt[30]{ a^{7} }\\---------------\)
5. \(\dfrac{q^{\frac{5}{4}}}{q^{-2}}\\= q^{ \frac{5}{4} - (-2) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-1}{5}}}\\= x^{ 1 - (\frac{-1}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)
8. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{1}{3}}}\\= q^{ \frac{5}{6} - \frac{1}{3} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\dfrac{y^{-1}}{y^{\frac{2}{5}}}\\= y^{ -1 - \frac{2}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{-5}{2}}}\\= y^{ -1 - (\frac{-5}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
11. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{5}{2} - (\frac{-1}{5}) }= q^{\frac{27}{10}}\\=\sqrt[10]{ q^{27} }=|q^{2}|.\sqrt[10]{ q^{7} }\\---------------\)
12. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{2} - (\frac{-1}{2}) }= x^{3}\\\\---------------\)