# Rekenregels machten

#### Pas de correcte rekenregel(s) van machten toe [en reken uit indien mogelijk]

1. $$(11x^{5})^{5}$$
2. $$-(-20)^{-6}$$
3. $$(\frac{14}{11}c)^{-3}:(\frac{14}{11}c)^{-7}$$
4. $$(-1y^{9})^{-2}$$
5. $$(2y)^{6}:(2y)^{-6}$$
6. $$(\frac{4}{5})^{-3}.(\frac{2}{5})^{-3}$$
7. $$(\frac{10}{7})^{-6}.(\frac{6}{19})^{-6}$$
8. $$(10a^{2})^{-6}$$
9. $$(\frac{7}{8}x)^{-7}.(\frac{7}{8}x)^{6}$$
10. $$(\frac{3}{4})^{7}.(\frac{19}{11})^{7}$$
11. $$(\frac{7}{12}b)^{-10}.(\frac{7}{12}b)^{-4}$$
12. $$(\frac{14}{5}x)^{-7}.(\frac{14}{5}x)^{-8}$$

#### Pas de correcte rekenregel(s) van machten toe [en reken uit indien mogelijk]

##### Verbetersleutel

1. $$(11x^{5})^{5}=(11)^{5}.(x^{5})^{5}=\text{ZRM}\left[=161051x^{25}\right]$$
2. $$-(-20)^{-6}=-(-\frac{1}{20})^{6}=-\frac{1^{6}}{20^{6}}=\text{ZRM}\left[=-\frac{1}{64000000}\right]$$
3. $$(\frac{14}{11}c)^{-3}:(\frac{14}{11}c)^{-7}=(\frac{14}{11}c)^{-3-(-7)}=(\frac{14}{11}c)^{4}=\text{ZRM}\left[ =\frac{38416}{14641}c^{4} \right]$$
4. $$(-1y^{9})^{-2}=(-1)^{-2}.(y^{9})^{-2}=(\frac{1}{-1})^{2}.(\frac{1}{y^{9}})^{2}=\text{ZRM}\left[=1 \frac{1}{y^{18}}\right]$$
5. $$(2y)^{6}:(2y)^{-6}=(2y)^{6-(-6)}=(2y)^{12}=\text{ZRM}\left[ =4096y^{12} \right]$$
6. $$(\frac{4}{5})^{-3}.(\frac{2}{5})^{-3}=(\frac{4}{5}\frac{2}{5})^{-3}=(\frac{8}{25})^{-3}=(\frac{25}{8})^{3}=\text{ZRM}=\left[\frac{15625}{512}\right]$$
7. $$(\frac{10}{7})^{-6}.(\frac{6}{19})^{-6}=(\frac{10}{7}\frac{6}{19})^{-6}=(\frac{60}{133})^{-6}=(\frac{133}{60})^{6}=\text{ZRM}=\left[\frac{5534900853769}{46656000000}\right]$$
8. $$(10a^{2})^{-6}=(10)^{-6}.(a^{2})^{-6}=(\frac{1}{10})^{6}.(\frac{1}{a^{2}})^{6}=\text{ZRM}\left[=\frac{1}{1000000} \frac{1}{a^{12}}\right]$$
9. $$(\frac{7}{8}x)^{-7}.(\frac{7}{8}x)^{6}=(\frac{7}{8}x)^{-7+6}=(\frac{7}{8}x)^{-1}=(\frac{8}{7}\frac{1}{x})^{1}\left[=\frac{8}{7} \frac{1}{x^{1}}\right]$$
10. $$(\frac{3}{4})^{7}.(\frac{19}{11})^{7}=(\frac{3}{4}\frac{19}{11})^{7}=(\frac{57}{44})^{7}=\text{ZRM}=\left[\frac{1954897493193}{319277809664}\right]$$
11. $$(\frac{7}{12}b)^{-10}.(\frac{7}{12}b)^{-4}=(\frac{7}{12}b)^{-10+(-4)}=(\frac{7}{12}b)^{-14}=(\frac{12}{7}\frac{1}{b})^{14}\left[=\frac{1283918464548864}{678223072849} \frac{1}{b^{14}}\right]=\text{ZRM}$$
12. $$(\frac{14}{5}x)^{-7}.(\frac{14}{5}x)^{-8}=(\frac{14}{5}x)^{-7+(-8)}=(\frac{14}{5}x)^{-15}=(\frac{5}{14}\frac{1}{x})^{15}\left[=\frac{30517578125}{155568095557812224} \frac{1}{x^{15}}\right]=\text{ZRM}$$
Oefeningengenerator vanhoeckes.be/wiskunde 2024-08-09 05:13:41