Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-2}{3} - \frac{1}{2} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-4}{5} - \frac{1}{3} }= x^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ x^{17} }}\\=\frac{1}{x.\sqrt[15]{ x^{2} }}=\frac{1}{x.\sqrt[15]{ x^{2} }} \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x^{2}}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{5}}}{a^{1}}\\= a^{ \frac{-3}{5} - 1 }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
5. \(\dfrac{a^{2}}{a^{\frac{-5}{6}}}\\= a^{ 2 - (\frac{-5}{6}) }= a^{\frac{17}{6}}\\=\sqrt[6]{ a^{17} }=|a^{2}|.\sqrt[6]{ a^{5} }\\---------------\)
6. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-4}{5} - \frac{5}{2} }= a^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ a^{33} }}\\=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{4}|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{4}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-2}{5} - (\frac{-1}{6}) }= x^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ x^{7} }}=\frac{1}{\sqrt[30]{ x^{7} }}. \color{purple}{\frac{\sqrt[30]{ x^{23} }}{\sqrt[30]{ x^{23} }}} \\=\frac{\sqrt[30]{ x^{23} }}{|x|}\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{1}{3}}}\\= x^{ -1 - \frac{1}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\dfrac{x^{\frac{5}{4}}}{x^{1}}\\= x^{ \frac{5}{4} - 1 }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
12. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{5} - (\frac{-1}{2}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)