Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{2} - (\frac{-1}{2}) }= x^{1}\\\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{-4}{3}}}\\= x^{ -1 - (\frac{-4}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
3. \(\dfrac{y^{\frac{5}{4}}}{y^{-1}}\\= y^{ \frac{5}{4} - (-1) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{2}}}\\= x^{ \frac{1}{2} - \frac{3}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
5. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-3}{2} - \frac{4}{5} }= a^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ a^{23} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a^{3} }}=\frac{1}{|a^{2}|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{3}|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-4}{5}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
7. \(\dfrac{y^{\frac{-3}{2}}}{y^{1}}\\= y^{ \frac{-3}{2} - 1 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
8. \(\dfrac{y^{2}}{y^{\frac{1}{3}}}\\= y^{ 2 - \frac{1}{3} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
9. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{4} - \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
10. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{2}{3}}}\\= q^{ \frac{5}{6} - \frac{2}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{1}{6}}}\\= a^{ \frac{5}{6} - \frac{1}{6} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{3}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)