Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{4}}}{x^{-2}}\\= x^{ \frac{-5}{4} - (-2) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
2. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{1}{3} - \frac{5}{4} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
3. \(\dfrac{q^{\frac{2}{3}}}{q^{-1}}\\= q^{ \frac{2}{3} - (-1) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{2} - (\frac{-1}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
5. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{3}{5}}}\\= q^{ \frac{-3}{4} - \frac{3}{5} }= q^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ q^{27} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{7} }}=\frac{1}{|q|.\sqrt[20]{ q^{7} }} \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{1}{3} - \frac{5}{6} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
8. \(\dfrac{x^{1}}{x^{-2}}\\= x^{ 1 - (-2) }= x^{3}\\\\---------------\)
9. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-2}{3} - \frac{2}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{4}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
11. \(\dfrac{a^{-1}}{a^{\frac{-1}{3}}}\\= a^{ -1 - (\frac{-1}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
12. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-3}{2} - \frac{1}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)