C Упростить 7,2a6b-710-468 5ab6 0,2a-36-4 (x²y-3)²-2x-4y-2 (10a²b²)-2-(3ab²)3 (3x-6y3)4xy-8 81 (2ac-2)3. (-33)2 1 90a4b3. (3-1)-1 (x-2y3)(9x+y-9)-1 (3-8)(36) 5 (2x-5)-2x-103 (2x2y8)2.(xy-3)3 3 (ab3)-3.(4b-5)-2 2 (3x6y-2)3.(x²y)-3 (0,1a-4b2)² - 100a9b6 3,2a6b: (0,8a3b-3)

Решения:

1. $$7,2a^6b^{-7} \cdot 10^{-4}a^{-4}b^8 = 7,2 \cdot 10^{-4} \cdot a^{6-4} \cdot b^{-7+8} = 7,2 \cdot 10^{-4} \cdot a^2 \cdot b = {7,2a^2b\over 10000}$$


2. $$5ab^6 \cdot 0,2a^{-3}b^{-4} = 5 \cdot 0,2 \cdot a^{1-3} \cdot b^{6-4} = 1 \cdot a^{-2} \cdot b^2 = {b^2\over a^2}$$


3. $$({1\over 8}x^2y^{-3})^{-1} \cdot 2x^{-4}y^{-2} = 8x^{-2}y^{3} \cdot 2x^{-4}y^{-2} = 8 \cdot 2 \cdot x^{-2-4} \cdot y^{3-2} = 16x^{-6}y = {16y\over x^6}$$


4. $$(10a^2b^2)^{-2} \cdot (3ab^2)^3 = 10^{-2}a^{-4}b^{-4} \cdot 3^3a^3b^6 = {1\over 100} \cdot a^{-4+3} \cdot b^{-4+6} \cdot 27 = {27\over 100} \cdot a^{-1} \cdot b^2 = {27b^2\over 100a}$$


5. $$(3x^{-6}y^3)^4 \cdot {1\over 81}xy^{-8} = 3^4x^{-24}y^{12} \cdot {1\over 81}xy^{-8} = 81x^{-24}y^{12} \cdot {1\over 81}xy^{-8} = x^{-24+1} \cdot y^{12-8} = x^{-23}y^4 = {y^4\over x^{23}}$$


6. $$(2ac^{-2})^3 \cdot ({1\over 2}a^{-3}c^3)^2 = 2^3a^3c^{-6} \cdot ({1\over 2})^2a^{-6}c^6 = 8a^3c^{-6} \cdot {1\over 4}a^{-6}c^6 = 8 \cdot {1\over 4} \cdot a^{3-6} \cdot c^{-6+6} = 2 \cdot a^{-3} \cdot c^0 = 2a^{-3} = {2\over a^3}$$


7. $$90a^4b^3 \cdot ({1\over 3}a^{-1}b^{-1})^{-1} = 90a^4b^3 \cdot 3a^1b^1 = 90 \cdot 3 \cdot a^{4+1} \cdot b^{3+1} = 270a^5b^4$$


8. $$({2\over 3}x^{-2}y^3)^{-3} \cdot (9x^4y^{-9})^{-1} = ({3\over 2})^3x^{6}y^{-9} \cdot {1\over 9}x^{-4}y^{9} = {27\over 8}x^{6}y^{-9} \cdot {1\over 9}x^{-4}y^{9} = {27\over 8} \cdot {1\over 9} \cdot x^{6-4} \cdot y^{-9+9} = {3\over 8} \cdot x^2 \cdot y^0 = {3x^2\over 8}$$


9. $$({4\over 5}a^3b^{-8})^2 \cdot ({3\over 5}a^6)^{-1} = ({4\over 5})^2a^6b^{-16} \cdot ({5\over 3}a^{-6}) = {16\over 25}a^6b^{-16} \cdot {5\over 3}a^{-6} = {16\over 25} \cdot {5\over 3} \cdot a^{6-6} \cdot b^{-16} = {16\over 15} \cdot a^0 \cdot b^{-16} = {16\over 15b^{16}}$$


10. $$({2\over 3}x^{-5}y)^{-2} \cdot {7\over 5}x^{-10}y^3 = ({3\over 2})^2x^{10}y^{-2} \cdot {7\over 5}x^{-10}y^3 = {9\over 4}x^{10}y^{-2} \cdot {7\over 5}x^{-10}y^3 = {9\over 4} \cdot {7\over 5} \cdot x^{10-10} \cdot y^{-2+3} = {63\over 20} \cdot x^0 \cdot y = {63y\over 20}$$


11. $$({2\over 3}x^2y^8)^2 \cdot ({1\over 2}xy^{-3})^3 = ({2\over 3})^2x^4y^{16} \cdot ({1\over 2})^3x^3y^{-9} = {4\over 9}x^4y^{16} \cdot {1\over 8}x^3y^{-9} = {4\over 9} \cdot {1\over 8} \cdot x^{4+3} \cdot y^{16-9} = {1\over 18} \cdot x^7 \cdot y^7 = {x^7y^7\over 18}$$


12. $$({1\over 2}ab^3)^{-3} \cdot (4b^{-5})^{-2} = 2^3a^{-3}b^{-9} \cdot 4^{-2}b^{10} = 8a^{-3}b^{-9} \cdot {1\over 16}b^{10} = 8 \cdot {1\over 16} \cdot a^{-3} \cdot b^{-9+10} = {1\over 2}a^{-3}b = {b\over 2a^3}$$


13. $$(3x^6y^{-2})^3 \cdot (x^2y)^{-3} = 3^3x^{18}y^{-6} \cdot x^{-6}y^{-3} = 27x^{18}y^{-6} \cdot x^{-6}y^{-3} = 27 \cdot x^{18-6} \cdot y^{-6-3} = 27x^{12}y^{-9} = {27x^{12}\over y^9}$$


14. $$(0,1a^{-4}b^2)^2 \cdot 100a^9b^6 = (0,1)^2a^{-8}b^4 \cdot 100a^9b^6 = 0,01a^{-8}b^4 \cdot 100a^9b^6 = 0,01 \cdot 100 \cdot a^{-8+9} \cdot b^{4+6} = 1 \cdot a \cdot b^{10} = ab^{10}$$


15. $$3,2a^6b \div (0,8a^3b^{-3}) = {3,2a^6b\over 0,8a^3b^{-3}} = {3,2\over 0,8} \cdot a^{6-3} \cdot b^{1-(-3)} = 4 \cdot a^3 \cdot b^{1+3} = 4a^3b^4$$

Ответ: 1) $${7,2a^2b\over 10000}$$, 2) $${b^2\over a^2}$$, 3) $${16y\over x^6}$$, 4) $${27b^2\over 100a}$$, 5) $${y^4\over x^{23}}$$, 6) $${2\over a^3}$$, 7) $$270a^5b^4$$, 8) $${3x^2\over 8}$$, 9) $${16\over 15b^{16}}$$, 10) $${63y\over 20}$$, 11) $${x^7y^7\over 18}$$, 12) $${b\over 2a^3}$$, 13) $${27x^{12}\over y^9}$$, 14) $$ab^{10}$$, 15) $$4a^3b^4$$