# Quotiënt zelfde grondtal

#### Werk uit m.b.v. de rekenregels

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

#### Werk uit m.b.v. de rekenregels

##### Verbetersleutel

1. $$\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-1}{4} - (\frac{-4}{3}) }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------$$
2. $$\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{3} - (\frac{-3}{4}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------$$
3. $$\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-1}{3} - (\frac{-4}{3}) }= x^{1}\\\\---------------$$
4. $$\dfrac{q^{\frac{-5}{2}}}{q^{1}}\\= q^{ \frac{-5}{2} - 1 }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------$$
5. $$\dfrac{x^{\frac{5}{6}}}{x^{\frac{1}{5}}}\\= x^{ \frac{5}{6} - \frac{1}{5} }= x^{\frac{19}{30}}\\=\sqrt[30]{ x^{19} }\\---------------$$
6. $$\dfrac{q^{-2}}{q^{\frac{-1}{2}}}\\= q^{ -2 - (\frac{-1}{2}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------$$
7. $$\dfrac{x^{\frac{4}{3}}}{x^{-2}}\\= x^{ \frac{4}{3} - (-2) }= x^{\frac{10}{3}}\\=\sqrt[3]{ x^{10} }=x^{3}.\sqrt[3]{ x }\\---------------$$
8. $$\dfrac{x^{\frac{-1}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-1}{2} - \frac{5}{6} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------$$
9. $$\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------$$
10. $$\dfrac{x^{\frac{4}{3}}}{x^{1}}\\= x^{ \frac{4}{3} - 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------$$
11. $$\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{3}}}\\= q^{ \frac{1}{4} - \frac{5}{3} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------$$
12. $$\dfrac{x^{\frac{-3}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-3}{4} - \frac{1}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------$$
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 08:14:24