Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-2}{3} - (\frac{-3}{4}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
3. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{3} - (\frac{-2}{3}) }= a^{1}\\\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-2}{3} - \frac{2}{5} }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{-1}{4}}}\\= q^{ -1 - (\frac{-1}{4}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
7. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{2}{5}}}\\= q^{ \frac{3}{2} - \frac{2}{5} }= q^{\frac{11}{10}}\\=\sqrt[10]{ q^{11} }=|q|.\sqrt[10]{ q }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{1}}\\= y^{ \frac{-1}{2} - 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-5}{2} - \frac{4}{3} }= y^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ y^{23} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{3}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{4}|}\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{4}{5}}}\\= x^{ -1 - \frac{4}{5} }= x^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ x^{9} }}\\=\frac{1}{x.\sqrt[5]{ x^{4} }}=\frac{1}{x.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{5}{6} - (\frac{-1}{2}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{2} - \frac{1}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)