Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{2}{3} - (\frac{-3}{5}) }= x^{\frac{19}{15}}\\=\sqrt[15]{ x^{19} }=x.\sqrt[15]{ x^{4} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{1}{3} - (\frac{-1}{6}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\dfrac{y^{\frac{5}{3}}}{y^{-1}}\\= y^{ \frac{5}{3} - (-1) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{1}{3}}}{a^{-1}}\\= a^{ \frac{1}{3} - (-1) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{1}{5}}}\\= y^{ 1 - \frac{1}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-1}{6} - (\frac{-1}{6}) }= y^{0}\\=1\\---------------\)
7. \(\dfrac{a^{\frac{-5}{3}}}{a^{-1}}\\= a^{ \frac{-5}{3} - (-1) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
8. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-2}{3}) }= x^{0}\\=1\\---------------\)
9. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{4} - \frac{2}{3} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
10. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{5}{4} - (\frac{-5}{3}) }= a^{\frac{35}{12}}\\=\sqrt[12]{ a^{35} }=|a^{2}|.\sqrt[12]{ a^{11} }\\---------------\)
11. \(\dfrac{y^{\frac{-5}{4}}}{y^{2}}\\= y^{ \frac{-5}{4} - 2 }= y^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ y^{13} }}\\=\frac{1}{|y^{3}|.\sqrt[4]{ y }}=\frac{1}{|y^{3}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{4}|}\\---------------\)
12. \(\dfrac{x^{1}}{x^{\frac{3}{2}}}\\= x^{ 1 - \frac{3}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)