Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{6} - \frac{2}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
2. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-2}{3} - (\frac{-3}{4}) }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
3. \(\dfrac{y^{\frac{-5}{2}}}{y^{1}}\\= y^{ \frac{-5}{2} - 1 }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
4. \(\dfrac{a^{\frac{4}{5}}}{a^{1}}\\= a^{ \frac{4}{5} - 1 }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
5. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{2}{5} - (\frac{-2}{3}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{1}{4}}}\\= q^{ \frac{3}{2} - \frac{1}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-4}{5}) }= x^{\frac{7}{15}}\\=\sqrt[15]{ x^{7} }\\---------------\)
8. \(\dfrac{x^{\frac{5}{4}}}{x^{2}}\\= x^{ \frac{5}{4} - 2 }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
9. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{4} - \frac{2}{5} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
10. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-3}{5} - \frac{5}{3} }= x^{\frac{-34}{15}}\\=\frac{1}{\sqrt[15]{ x^{34} }}\\=\frac{1}{x^{2}.\sqrt[15]{ x^{4} }}=\frac{1}{x^{2}.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{3}}\\---------------\)
11. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-3}{2} - (\frac{-2}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{1}{2} - (\frac{-5}{3}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)