Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{4} - (\frac{-1}{4}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
2. \(\dfrac{q^{\frac{-1}{3}}}{q^{1}}\\= q^{ \frac{-1}{3} - 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-5}{3}) }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{-2}{3}}}\\= x^{ -1 - (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
5. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{2}{3} - (\frac{-3}{4}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
6. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{5} - \frac{4}{5} }= a^{-1}\\=\frac{1}{a}\\---------------\)
7. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{4}}}\\= q^{ \frac{1}{4} - \frac{5}{4} }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{5}}}{q^{-1}}\\= q^{ \frac{-1}{5} - (-1) }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-1}{2} - \frac{5}{4} }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{4}{3}}}\\= a^{ \frac{3}{5} - \frac{4}{3} }= a^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ a^{11} }}=\frac{1}{\sqrt[15]{ a^{11} }}. \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{6} - \frac{1}{2} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
12. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-3}{5} - (\frac{-1}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)