Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{-3}{5}}}\\= q^{ -1 - (\frac{-3}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{1}{2} - (\frac{-1}{5}) }= y^{\frac{7}{10}}\\=\sqrt[10]{ y^{7} }\\---------------\)
3. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-3}{5} - (\frac{-5}{4}) }= x^{\frac{13}{20}}\\=\sqrt[20]{ x^{13} }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{6} - (\frac{-1}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{x^{1}}{x^{\frac{-1}{2}}}\\= x^{ 1 - (\frac{-1}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
6. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{1}{3} - (\frac{-4}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
7. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-2}{3}) }= x^{0}\\=1\\---------------\)
8. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{5}{4} - (\frac{-2}{3}) }= q^{\frac{23}{12}}\\=\sqrt[12]{ q^{23} }=|q|.\sqrt[12]{ q^{11} }\\---------------\)
9. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{2}{3} - (\frac{-4}{5}) }= a^{\frac{22}{15}}\\=\sqrt[15]{ a^{22} }=a.\sqrt[15]{ a^{7} }\\---------------\)
10. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{2}{5} - (\frac{-3}{4}) }= x^{\frac{23}{20}}\\=\sqrt[20]{ x^{23} }=|x|.\sqrt[20]{ x^{3} }\\---------------\)
11. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)