Question

вычислите 5^4k*0,5^-2-2k/50^2k-1

Answer 1

0,5 ^ ( - 2 - 2K ) = 2 ^ ( - ( - 2 - 2K )) = 2 ^ ( 2 + 2K ) 
50 ^ ( 2K - 1 ) = ( 5 ^ 2 ) ^ ( 2K - 1 ) * 2 ^ ( 2K - 1 ) = 5 ^ ( 4K - 2 ) * 2 ^ ( 2K - 1 )
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[  ( 5 ^ 4K ) * ( 2 ^ ( 2 + 2K ) ] / [ ( 5 ^ 4K - 2 ) * ( 2 ^ ( 2K - 1 ) ] =
= 5 ^ ( 4K - ( 4K - 2 ) ) * 2 ^ ( 2 + 2K - ( 2K - 1 ) ) =
= 5 ^ 2 * 2 ^ 3 = 25 * 8 = 200
ОТВЕТ 200