Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-5}{3} - \frac{5}{3} }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{2}{3} - \frac{5}{4} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
3. \(\dfrac{q^{-2}}{q^{\frac{-4}{3}}}\\= q^{ -2 - (\frac{-4}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
4. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-4}{3} - \frac{5}{6} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{3}{5}}}{x^{1}}\\= x^{ \frac{3}{5} - 1 }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
6. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-5}{3} - (\frac{-1}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
7. \(\dfrac{y^{\frac{-4}{3}}}{y^{-1}}\\= y^{ \frac{-4}{3} - (-1) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-1}{6} - \frac{4}{5} }= y^{\frac{-29}{30}}\\=\frac{1}{\sqrt[30]{ y^{29} }}=\frac{1}{\sqrt[30]{ y^{29} }}. \color{purple}{\frac{\sqrt[30]{ y }}{\sqrt[30]{ y }}} \\=\frac{\sqrt[30]{ y }}{|y|}\\---------------\)
9. \(\dfrac{q^{2}}{q^{1}}\\= q^{ 2 - 1 }= q^{1}\\\\---------------\)
10. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-1}{4} - (\frac{-4}{3}) }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{2}{3} - (\frac{-3}{5}) }= a^{\frac{19}{15}}\\=\sqrt[15]{ a^{19} }=a.\sqrt[15]{ a^{4} }\\---------------\)
12. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{1}{4} - (\frac{-2}{3}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)