Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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