Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{6}}}{a^{1}}\\= a^{ \frac{1}{6} - 1 }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-3}{2} - \frac{1}{6} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{3}{5} - (\frac{-4}{5}) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{3} - \frac{3}{2} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-1}{2} - \frac{5}{3} }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{5}}}{x^{-2}}\\= x^{ \frac{-1}{5} - (-2) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
9. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-3}{4} - \frac{2}{5} }= y^{\frac{-23}{20}}\\=\frac{1}{\sqrt[20]{ y^{23} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{3} }}=\frac{1}{|y|.\sqrt[20]{ y^{3} }} \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-1}{6} - \frac{4}{3} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{3}{4}}}\\= q^{ \frac{2}{5} - \frac{3}{4} }= q^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ q^{7} }}=\frac{1}{\sqrt[20]{ q^{7} }}. \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q|}\\---------------\)
12. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{2}{5} - \frac{1}{3} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)