Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{5}{6} - \frac{1}{2} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
2. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-3}{2} - (\frac{-3}{5}) }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}. \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{-2}}\\= q^{ \frac{-2}{3} - (-2) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-4}{3}) }= q^{1}\\\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{-1}}\\= y^{ \frac{2}{3} - (-1) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
7. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-5}{6} - \frac{1}{2} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
8. \(\dfrac{q^{\frac{-2}{5}}}{q^{-1}}\\= q^{ \frac{-2}{5} - (-1) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
9. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{5}{4} - (\frac{-3}{5}) }= x^{\frac{37}{20}}\\=\sqrt[20]{ x^{37} }=|x|.\sqrt[20]{ x^{17} }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
11. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-4}{3} - \frac{5}{2} }= a^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ a^{23} }}\\=\frac{1}{|a^{3}|.\sqrt[6]{ a^{5} }}=\frac{1}{|a^{3}|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{4}|}\\---------------\)
12. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{2} - (\frac{-1}{2}) }= x^{3}\\\\---------------\)