Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{3}{2}}}\\= q^{ 1 - \frac{3}{2} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-4}{3} - (\frac{-2}{5}) }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-1}{2} - \frac{5}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
5. \(\dfrac{a^{-1}}{a^{\frac{-5}{2}}}\\= a^{ -1 - (\frac{-5}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
6. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-3}{5} - \frac{4}{3} }= x^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ x^{29} }}\\=\frac{1}{x.\sqrt[15]{ x^{14} }}=\frac{1}{x.\sqrt[15]{ x^{14} }} \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x^{2}}\\---------------\)
7. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{3}{2} - \frac{3}{5} }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
8. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{2}{5} - \frac{1}{3} }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
9. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-3}{4} - (\frac{-4}{5}) }= q^{\frac{1}{20}}\\=\sqrt[20]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-4}{5} - \frac{1}{2} }= y^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{3} }}=\frac{1}{|y|.\sqrt[10]{ y^{3} }} \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{4}{3}}}\\= q^{ \frac{2}{5} - \frac{4}{3} }= q^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ q^{14} }}=\frac{1}{\sqrt[15]{ q^{14} }}. \color{purple}{\frac{\sqrt[15]{ q }}{\sqrt[15]{ q }}} \\=\frac{\sqrt[15]{ q }}{q}\\---------------\)
12. \(\dfrac{x^{\frac{2}{3}}}{x^{-1}}\\= x^{ \frac{2}{3} - (-1) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)