# Product zelfde grondtal

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

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

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

##### Verbetersleutel

1. $$x^{\frac{-1}{5}}.x^{\frac{1}{2}}\\= x^{ \frac{-1}{5} + \frac{1}{2} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------$$
2. $$a^{-1}.a^{\frac{-3}{2}}\\= a^{ -1 + (\frac{-3}{2}) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------$$
3. $$x^{\frac{-1}{2}}.x^{\frac{-3}{5}}\\= x^{ \frac{-1}{2} + (\frac{-3}{5}) }= x^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[10]{ x }}=\frac{1}{|x|.\sqrt[10]{ x }} \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x^{2}|}\\---------------$$
4. $$y^{\frac{1}{2}}.y^{1}\\= y^{ \frac{1}{2} + 1 }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------$$
5. $$x^{\frac{-3}{5}}.x^{\frac{-1}{4}}\\= x^{ \frac{-3}{5} + (\frac{-1}{4}) }= x^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ x^{17} }}=\frac{1}{\sqrt[20]{ x^{17} }}. \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x|}\\---------------$$
6. $$a^{\frac{1}{5}}.a^{\frac{-3}{2}}\\= a^{ \frac{1}{5} + (\frac{-3}{2}) }= a^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{3} }}=\frac{1}{|a|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{2}|}\\---------------$$
7. $$a^{-2}.a^{-1}\\= a^{ -2 + (-1) }= a^{-3}\\=\frac{1}{a^{3}}\\---------------$$
8. $$q^{\frac{5}{2}}.q^{\frac{-2}{3}}\\= q^{ \frac{5}{2} + (\frac{-2}{3}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------$$
9. $$y^{\frac{3}{2}}.y^{\frac{3}{5}}\\= y^{ \frac{3}{2} + \frac{3}{5} }= y^{\frac{21}{10}}\\=\sqrt[10]{ y^{21} }=|y^{2}|.\sqrt[10]{ y }\\---------------$$
10. $$y^{\frac{-1}{5}}.y^{\frac{-1}{2}}\\= y^{ \frac{-1}{5} + (\frac{-1}{2}) }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------$$
11. $$y^{\frac{-5}{3}}.y^{\frac{-1}{3}}\\= y^{ \frac{-5}{3} + (\frac{-1}{3}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------$$
12. $$q^{\frac{-1}{4}}.q^{\frac{5}{2}}\\= q^{ \frac{-1}{4} + \frac{5}{2} }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------$$
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 07:07:09