Решить подробно. №1. а) (1/4)⁻¹/²×25¹/2- 81¹/²×125⁻¹/³ б)49⁻¹/²×(1/7)⁻²+2⁻¹×(-2)⁻² в)216⁻¹/³×(1/6)⁻² - 5⁻¹×(1/25)⁻¹/² г)(1/4)⁻¹/²×16⁻¹/²- 2⁻¹× (1/25)⁻¹/²×8⁻¹/³ №2 а) ( (1/25)⁻¹/²×7⁻¹ - (1/8)⁻¹/³×2⁻³): 49⁻¹/² б) 8¹/³×25⁻¹/² - 2⁻¹ и всё это делить на 64¹/⁴×2¹/².

а) (1/4)⁻¹/²×25¹/2- 81¹/²×125⁻¹/³ =
=(2^(-2))^(-1/2) * (5^2)^(1/2)-(9^2)^(1/2)*(5^3)^(-1/3)=
=2^1 * 5^1-9^1*5^(-1)= 10-9/5=9-4/5=8+1/5=8,2
б)49⁻¹/²×(1/7)⁻²+2⁻¹×(-2)⁻² =
=(7^2)^(-1/2)×(7^(-1))^(-2)+2^(-1)×(-1)^(-2)*(2)^(-2) =
=7^(-1)×7^(2)+2^(-1)×(2)^(-2) =
=7^(1)+2^(-3) = 7+1/8=7,125

в)216⁻¹/³×(1/6)⁻² - 5⁻¹×(1/25)⁻¹/²=
=(6^3)^(-1/3)×(6^(-1))^(-2) - 5^(-1)×(5^(-2))^(-1/2)=
=(6^(-1))×(6^2) - 5^(-1)×(5^(1))=
=6^1 - 5^0= 6-1=5

г)(1/4)⁻¹/²×16⁻¹/²- 2⁻¹× (1/25)⁻¹/²×8⁻¹/³=
=(2^(-2))^(-1/2)×(2^4)^(-1/2)- (2^(-1)× (5^(-2))^(-1/2)×(2^3)^(-1/3)=
=2^(1)×2^(-2)- 2^(-1)× 5^1×2^(-1)=
=2^(-1)- 2^(-2)× 5=0,5-5/4=0,5-1,25=-0,75

№2

а) ( (1/25)⁻¹/²×7⁻¹ - (1/8)⁻¹/³×2⁻³):49⁻¹/²=
=( (5^(-2))^(-1/2)×7^(-1) - (2^(-3))^(-1/3)×2^(-3))/((7^2)^(-1/2)=
=( (5^1)×7^(-1) - (2^1)×2^(-3))*7=
=5 - 7/4=3,25

б) 8¹/³×25⁻¹/² - 2⁻¹ и всё это делить на 64¹/⁴×2¹/².=
=(2/5 - 0,5)/(2^(6/4+1/2))=
= - 0,1/2^2=-0,025