Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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