Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-3}{5}}}{x^{1}}\\= x^{ \frac{-3}{5} - 1 }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
3. \(\dfrac{q^{1}}{q^{\frac{4}{3}}}\\= q^{ 1 - \frac{4}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
4. \(\dfrac{x^{-2}}{x^{\frac{1}{3}}}\\= x^{ -2 - \frac{1}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
5. \(\dfrac{y^{\frac{-3}{2}}}{y^{-2}}\\= y^{ \frac{-3}{2} - (-2) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-2}{3} - \frac{4}{5} }= a^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ a^{22} }}\\=\frac{1}{a.\sqrt[15]{ a^{7} }}=\frac{1}{a.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-5}{6} - \frac{1}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{5}{3} - (\frac{-1}{2}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
9. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{2}{5}}}\\= q^{ \frac{5}{6} - \frac{2}{5} }= q^{\frac{13}{30}}\\=\sqrt[30]{ q^{13} }\\---------------\)
10. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{1}{2} - (\frac{-2}{3}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-5}{3} - (\frac{-2}{5}) }= q^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ q^{19} }}\\=\frac{1}{q.\sqrt[15]{ q^{4} }}=\frac{1}{q.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{2}}\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{-1}{6}}}\\= a^{ 1 - (\frac{-1}{6}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)