Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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