Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{2}}{q^{\frac{1}{3}}}\\= q^{ 2 - \frac{1}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
2. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{5}{3} - \frac{1}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{1}{4} - (\frac{-3}{5}) }= x^{\frac{17}{20}}\\=\sqrt[20]{ x^{17} }\\---------------\)
5. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
6. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{3}{2} - (\frac{-2}{5}) }= a^{\frac{19}{10}}\\=\sqrt[10]{ a^{19} }=|a|.\sqrt[10]{ a^{9} }\\---------------\)
7. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{4}{5} - (\frac{-1}{2}) }= q^{\frac{13}{10}}\\=\sqrt[10]{ q^{13} }=|q|.\sqrt[10]{ q^{3} }\\---------------\)
8. \(\dfrac{q^{\frac{-3}{4}}}{q^{1}}\\= q^{ \frac{-3}{4} - 1 }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{4} - (\frac{-1}{3}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
10. \(\dfrac{x^{\frac{-5}{6}}}{x^{1}}\\= x^{ \frac{-5}{6} - 1 }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{4} - \frac{5}{6} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)