Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{5}{6}}}\\= x^{ \frac{5}{4} - \frac{5}{6} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
2. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{5}{6}}}\\= a^{ \frac{5}{6} - \frac{5}{6} }= a^{0}\\=1\\---------------\)
3. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{3} - \frac{2}{5} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
4. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-5}{6} - (\frac{-3}{2}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{3} - \frac{1}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{2} - (\frac{-2}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-3}{5} - \frac{2}{3} }= q^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ q^{19} }}\\=\frac{1}{q.\sqrt[15]{ q^{4} }}=\frac{1}{q.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{5}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
9. \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\\= q^{ \frac{5}{4} - 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
10. \(\dfrac{q^{\frac{-4}{5}}}{q^{2}}\\= q^{ \frac{-4}{5} - 2 }= q^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ q^{14} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }}=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{3}}\\---------------\)
11. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{5}{2} - \frac{1}{3} }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
12. \(\dfrac{x^{\frac{4}{3}}}{x^{1}}\\= x^{ \frac{4}{3} - 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)