Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
2. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{3}{4} - (\frac{-1}{6}) }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
3. \(\dfrac{q^{-2}}{q^{\frac{-2}{3}}}\\= q^{ -2 - (\frac{-2}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{1}{2} - (\frac{-5}{2}) }= q^{3}\\\\---------------\)
5. \(\dfrac{a^{\frac{-1}{3}}}{a^{1}}\\= a^{ \frac{-1}{3} - 1 }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{5}{2}}}{a^{-2}}\\= a^{ \frac{5}{2} - (-2) }= a^{\frac{9}{2}}\\= \sqrt{ a^{9} } =|a^{4}|. \sqrt{ a } \\---------------\)
7. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-1}{3} - \frac{3}{4} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{5}}}\\= a^{ \frac{1}{3} - \frac{1}{5} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{-1}}\\= x^{ \frac{-1}{3} - (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
10. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-2}{5} - \frac{2}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{4}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{2}{3}}}\\= a^{ -1 - \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)