# Getallen als grondtal

#### Bereken m.b.v. de rekenregels (zonder ZRM)

1. $$\sqrt{ (\frac{3}{2})^{8} }$$
2. $$\sqrt[3]{ (\frac{5}{4})^{6} }$$
3. $$\sqrt[4]{ (\frac{2}{3})^{16} }$$
4. $$\sqrt[4]{ (\frac{49}{81})^{2} }$$
5. $$\sqrt[6]{ (8)^{2} }$$
6. $$\sqrt[4]{ (\frac{4}{3})^{12} }$$
7. $$\sqrt[6]{ (\frac{1}{9})^{3} }$$
8. $$\sqrt[4]{ (\frac{2}{3})^{-12} }$$
9. $$\sqrt[6]{ (\frac{8}{27})^{2} }$$
10. $$\sqrt[6]{ (\frac{196}{361})^{3} }$$
11. $$\sqrt[4]{ (\frac{3}{2})^{16} }$$
12. $$\sqrt[12]{ (\frac{64}{27})^{4} }$$

#### Bereken m.b.v. de rekenregels (zonder ZRM)

##### Verbetersleutel

1. $$\sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}$$
2. $$\sqrt[3]{ (\frac{5}{4})^{6} }\\= (\frac{5}{4})^{\frac{6}{3}}\\= (\frac{5}{4})^{2}=\frac{25}{16}$$
3. $$\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}$$
4. $$\sqrt[4]{ (\frac{49}{81})^{2} }\\= (\frac{49}{81})^{\frac{2}{4}}\\= (\frac{49}{81})^{\frac{1}{2}}\\= \sqrt{ \frac{49}{81} } =\frac{7}{9}$$
5. $$\sqrt[6]{ (8)^{2} }\\= (8)^{\frac{-2}{6}}\\= (8)^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}$$
6. $$\sqrt[4]{ (\frac{4}{3})^{12} }\\= (\frac{4}{3})^{\frac{12}{4}}\\= (\frac{4}{3})^{3}=\frac{64}{27}$$
7. $$\sqrt[6]{ (\frac{1}{9})^{3} }\\= (\frac{1}{9})^{\frac{3}{6}}\\= (\frac{1}{9})^{\frac{1}{2}}\\= \sqrt{ \frac{1}{9} } =\frac{1}{3}$$
8. $$\sqrt[4]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{4}}\\= (\frac{2}{3})^{-3}\\= (\frac{3}{2})^{3}= \frac{27}{8}$$
9. $$\sqrt[6]{ (\frac{8}{27})^{2} }\\= (\frac{8}{27})^{\frac{2}{6}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}$$
10. $$\sqrt[6]{ (\frac{196}{361})^{3} }\\= (\frac{196}{361})^{\frac{-3}{6}}\\= (\frac{196}{361})^{\frac{-1}{2}}\\= \sqrt{ \frac{361}{196} } =\frac{19}{14}$$
11. $$\sqrt[4]{ (\frac{3}{2})^{16} }\\= (\frac{3}{2})^{\frac{16}{4}}\\= (\frac{3}{2})^{4}=\frac{81}{16}$$
12. $$\sqrt[12]{ (\frac{64}{27})^{4} }\\= (\frac{64}{27})^{\frac{-4}{12}}\\= (\frac{64}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}$$
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 02:28:01