Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
2. \(\dfrac{y^{-2}}{y^{\frac{1}{2}}}\\= y^{ -2 - \frac{1}{2} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
3. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{5}{2} - \frac{2}{3} }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
4. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-2}{5} - (\frac{-3}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-1}{3} - \frac{5}{2} }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
6. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{5}{3} - \frac{2}{5} }= y^{\frac{19}{15}}\\=\sqrt[15]{ y^{19} }=y.\sqrt[15]{ y^{4} }\\---------------\)
7. \(\dfrac{q^{2}}{q^{\frac{-1}{3}}}\\= q^{ 2 - (\frac{-1}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
8. \(\dfrac{q^{2}}{q^{1}}\\= q^{ 2 - 1 }= q^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{5}{2} - (\frac{-5}{3}) }= y^{\frac{25}{6}}\\=\sqrt[6]{ y^{25} }=|y^{4}|.\sqrt[6]{ y }\\---------------\)
11. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{5}{6} - (\frac{-3}{5}) }= q^{\frac{43}{30}}\\=\sqrt[30]{ q^{43} }=|q|.\sqrt[30]{ q^{13} }\\---------------\)
12. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{1}{6}}}\\= a^{ \frac{-2}{3} - \frac{1}{6} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)