Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{5}}}{y^{1}}\\= y^{ \frac{-4}{5} - 1 }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
2. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{2}{5} - (\frac{-5}{3}) }= y^{\frac{31}{15}}\\=\sqrt[15]{ y^{31} }=y^{2}.\sqrt[15]{ y }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-1}{2} - \frac{5}{4} }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-4}{3} - (\frac{-4}{3}) }= y^{0}\\=1\\---------------\)
5. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{3} - \frac{4}{5} }= x^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ x^{17} }}\\=\frac{1}{x.\sqrt[15]{ x^{2} }}=\frac{1}{x.\sqrt[15]{ x^{2} }} \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{1}{2}}}{a^{-2}}\\= a^{ \frac{1}{2} - (-2) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
7. \(\dfrac{y^{-1}}{y^{\frac{2}{5}}}\\= y^{ -1 - \frac{2}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{1}{5}}}\\= a^{ 1 - \frac{1}{5} }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-3}{2}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{2}{3} - (\frac{-5}{2}) }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{5}{3} - \frac{2}{3} }= x^{1}\\\\---------------\)