Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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