Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-5}{4} - (\frac{-1}{2}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
2. \(\dfrac{q^{\frac{5}{2}}}{q^{-1}}\\= q^{ \frac{5}{2} - (-1) }= q^{\frac{7}{2}}\\= \sqrt{ q^{7} } =|q^{3}|. \sqrt{ q } \\---------------\)
3. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{3}{5}}}\\= q^{ \frac{1}{2} - \frac{3}{5} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
4. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{2}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{4}}}{y^{1}}\\= y^{ \frac{-1}{4} - 1 }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{3} - (\frac{-1}{2}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-3}{2} - (\frac{-4}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{3}{2}}}\\= y^{ 1 - \frac{3}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{5}{4}}}\\= q^{ 1 - \frac{5}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
10. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{5}{3} - (\frac{-3}{5}) }= y^{\frac{34}{15}}\\=\sqrt[15]{ y^{34} }=y^{2}.\sqrt[15]{ y^{4} }\\---------------\)
11. \(\dfrac{x^{\frac{-5}{2}}}{x^{-1}}\\= x^{ \frac{-5}{2} - (-1) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{2} - (\frac{-2}{5}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)