Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{2}{3} - \frac{5}{4} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{2}{5} - \frac{3}{2} }= q^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[10]{ q }}=\frac{1}{|q|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-5}{2} - \frac{3}{5} }= x^{\frac{-31}{10}}\\=\frac{1}{\sqrt[10]{ x^{31} }}\\=\frac{1}{|x^{3}|.\sqrt[10]{ x }}=\frac{1}{|x^{3}|.\sqrt[10]{ x }} \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x^{4}|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{4} - \frac{1}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{2} - \frac{2}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{5}{6} - (\frac{-4}{3}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{5}{2}}}\\= x^{ -1 - \frac{5}{2} }= x^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ x^{7} } }\\=\frac{1}{|x^{3}|. \sqrt{ x } }=\frac{1}{|x^{3}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{4}|}\\---------------\)
8. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-4}{5} - (\frac{-2}{3}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
9. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-5}{4} - (\frac{-2}{3}) }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{5}{4}}}\\= y^{ \frac{1}{2} - \frac{5}{4} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-2}{5}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{4}{5}}}\\= y^{ -1 - \frac{4}{5} }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)