Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-5}{3} - (\frac{-2}{3}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{1}{2} - (\frac{-5}{4}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
3. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{3}{4} - (\frac{-5}{2}) }= a^{\frac{13}{4}}\\=\sqrt[4]{ a^{13} }=|a^{3}|.\sqrt[4]{ a }\\---------------\)
4. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-3}{5} - \frac{3}{4} }= q^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ q^{27} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{7} }}=\frac{1}{|q|.\sqrt[20]{ q^{7} }} \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-4}{5} - (\frac{-5}{3}) }= q^{\frac{13}{15}}\\=\sqrt[15]{ q^{13} }\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{5}{2}}}\\= a^{ \frac{1}{3} - \frac{5}{2} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{4} - \frac{1}{4} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-4}{3} - (\frac{-5}{2}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{1}}\\= x^{ \frac{4}{5} - 1 }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
10. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-2}{3} - \frac{1}{4} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
11. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{3} - \frac{3}{5} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
12. \(\dfrac{q^{\frac{1}{5}}}{q^{-1}}\\= q^{ \frac{1}{5} - (-1) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)