Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-4}{5} - \frac{5}{4} }= y^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ y^{41} }}\\=\frac{1}{|y^{2}|.\sqrt[20]{ y }}=\frac{1}{|y^{2}|.\sqrt[20]{ y }} \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{4} - \frac{1}{3} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{-2}{3}}}\\= a^{ -1 - (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
4. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{4}{5} - \frac{1}{6} }= y^{\frac{19}{30}}\\=\sqrt[30]{ y^{19} }\\---------------\)
5. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{5}{4} - (\frac{-2}{5}) }= x^{\frac{33}{20}}\\=\sqrt[20]{ x^{33} }=|x|.\sqrt[20]{ x^{13} }\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{1}{3}}}\\= y^{ 1 - \frac{1}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{5}}}{q^{-2}}\\= q^{ \frac{-1}{5} - (-2) }= q^{\frac{9}{5}}\\=\sqrt[5]{ q^{9} }=q.\sqrt[5]{ q^{4} }\\---------------\)
8. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{4}{3} - \frac{3}{5} }= x^{\frac{11}{15}}\\=\sqrt[15]{ x^{11} }\\---------------\)
9. \(\dfrac{y^{\frac{1}{6}}}{y^{1}}\\= y^{ \frac{1}{6} - 1 }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
10. \(\dfrac{q^{-2}}{q^{1}}\\= q^{ -2 - 1 }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
11. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{5}{6} - (\frac{-4}{3}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
12. \(\dfrac{q^{\frac{-5}{6}}}{q^{1}}\\= q^{ \frac{-5}{6} - 1 }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)