Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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