Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{3}}}{x^{-1}}\\= x^{ \frac{5}{3} - (-1) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)
2. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-2}{5} - (\frac{-1}{3}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{2} - \frac{1}{5} }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)
4. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{2}{3} - (\frac{-1}{4}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{5} - (\frac{-2}{3}) }= a^{\frac{7}{15}}\\=\sqrt[15]{ a^{7} }\\---------------\)
6. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
7. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-5}{3} - \frac{2}{5} }= a^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ a^{31} }}\\=\frac{1}{a^{2}.\sqrt[15]{ a }}=\frac{1}{a^{2}.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{3}}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-3}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
9. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-3}{4} - (\frac{-1}{3}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
10. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-5}{4} - (\frac{-1}{2}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
11. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{1}{5} - \frac{5}{4} }= x^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ x^{21} }}\\=\frac{1}{|x|.\sqrt[20]{ x }}=\frac{1}{|x|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{x^{1}}{x^{\frac{-1}{3}}}\\= x^{ 1 - (\frac{-1}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)