Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{3}{2}}}\\= y^{ 1 - \frac{3}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-1}{2} - \frac{1}{6} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
4. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{4}{3} - \frac{1}{2} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{2} - \frac{4}{5} }= a^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{3} }}=\frac{1}{|a|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{4} - (\frac{-5}{6}) }= a^{\frac{7}{12}}\\=\sqrt[12]{ a^{7} }\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{1}{3}}}\\= a^{ 1 - \frac{1}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-4}{3} - (\frac{-4}{3}) }= y^{0}\\=1\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{4}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{1}{5}}}\\= q^{ 1 - \frac{1}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
12. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-2}{5} - \frac{1}{4} }= x^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ x^{13} }}=\frac{1}{\sqrt[20]{ x^{13} }}. \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x|}\\---------------\)