A Вычислить √5·4·56 √45·4-7 383-53-6 69:611 √7-4:7-4 8-6:8-7 √(3-2)-2 (0,1-3)-1 (0,2-2)3 (72)-3.74 √5-3.(5-2)-3 5 (3):(3) 3

Решения:

1. $$√5\cdot4\cdot56 = √1120$$


2. $$√45\cdot4^{-7} = √{45\over 4^7} = {√45 \over √4^7} = {√45 \over 2^7} = {√45 \over 128}$$


3. $$38^3 \cdot 3^{-5} \cdot 3^{-6} = 38^{3-5-6} = 38^{-8} = {1\over 38^8}$$


4. $$6^9 : 6^{11} = 6^{9-11} = 6^{-2} = {1 \over 6^2} = {1 \over 36}$$


5. $$√7^{-4} : 7^{-4} = √{7^{-4} \over 7^{-4}} = √1 = 1$$


6. $$8^{-6} : 8^{-7} = 8^{-6-(-7)} = 8^{-6+7} = 8^1 = 8$$


7. $$√(3^{-2})^{-2} = √(3^{(-2) \cdot (-2)}) = √3^4 = √81 = 9$$


8. $$(0,1)^{-3} = ({1\over 10})^{-3} = ({10\over 1})^3 = 10^3 = 1000$$


9. $$(0,2)^{-2})^3 = ({2\over 10})^{-2})^3 = ({1\over 5})^{-6} = 5^6 = 15625$$


10. $$(7^2)^{-3} \cdot 7^4 = 7^{2 \cdot (-3)} \cdot 7^4 = 7^{-6} \cdot 7^4 = 7^{-6+4} = 7^{-2} = {1 \over 7^2} = {1\over 49}$$


11. $$√5^{-3} \cdot (5^{-2})^{-3} = √5^{-3} \cdot 5^{(-2) \cdot (-3)} = √5^{-3} \cdot 5^6 = √5^{-3+6} = √5^3 = √125$$


12. $$({1\over 4})^{-5} = ({4\over 1})^5 = 4^5 = 1024$$


13. $$({1\over 3})^3 \div ({1\over 3})^{-6} = ({1\over 3})^{3 - (-6)} = ({1\over 3})^{3+6} = ({1\over 3})^9 = {1\over 3^9} = {1\over 19683}$$

Ответ: 1) $$√1120$$, 2) $${√45 \over 128}$$, 3) $${1\over 38^8}$$, 4) $${1 \over 36}$$, 5) $$1$$, 6) $$8$$, 7) $$9$$, 8) $$1000$$, 9) $$15625$$, 10) $${1\over 49}$$, 11) $$√125$$, 12) $$1024$$, 13) $${1\over 19683}$$