Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-3}{5} - \frac{3}{4} }= x^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ x^{27} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{7} }}=\frac{1}{|x|.\sqrt[20]{ x^{7} }} \color{purple}{\frac{\sqrt[20]{ x^{13} }}{\sqrt[20]{ x^{13} }}} \\=\frac{\sqrt[20]{ x^{13} }}{|x^{2}|}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
3. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{2} - (\frac{-1}{2}) }= a^{2}\\\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{3}{4}}}\\= y^{ \frac{1}{2} - \frac{3}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{2} - \frac{5}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{4}{3} - (\frac{-1}{2}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
7. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-2}{5} - \frac{2}{5} }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{1}{2} - \frac{1}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{2}{5} - \frac{5}{2} }= a^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ a^{21} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a }}=\frac{1}{|a^{2}|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{3}|}\\---------------\)
10. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-2}{5} - \frac{4}{5} }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{3}{4} - \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{5}}}\\= q^{ \frac{1}{2} - \frac{1}{5} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)