Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-3}{2} - \frac{4}{5} }= a^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ a^{23} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a^{3} }}=\frac{1}{|a^{2}|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{6} - \frac{1}{4} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{1}}\\= y^{ \frac{-1}{2} - 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{2} - \frac{1}{3} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-4}{3} - \frac{3}{5} }= x^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ x^{29} }}\\=\frac{1}{x.\sqrt[15]{ x^{14} }}=\frac{1}{x.\sqrt[15]{ x^{14} }} \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x^{2}}\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{5}{4}}}\\= q^{ 1 - \frac{5}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{5} - \frac{1}{2} }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{-3}{5}}}\\= x^{ 1 - (\frac{-3}{5}) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
9. \(\dfrac{y^{-1}}{y^{\frac{-5}{4}}}\\= y^{ -1 - (\frac{-5}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
10. \(\dfrac{a^{2}}{a^{2}}\\= a^{ 2 - 2 }= a^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{2} - (\frac{-5}{4}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{6}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)