Сократите дробь:
[tex] \frac{( 5^{1-5n})*( 4^{2n+1} )*( 2,5)^{11n} }{160} [/tex]
[tex] \frac{( 5^{1-5n})*( 4^{2n+1} )*( 2,5)^{11n} }{160} [/tex]
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4 ^(2n+1)=4^2n * 4(4^2)^n=(4^2) *(4^2)^(n-1)
т.е. вместо 4 ^(2n+1) получается 4* (4^2) *(4^2)^(n-1)=4*16*(4^2)^(n-1)
2,5 ^ 11n=2.5 * 2.5^(11n-1)
(5^(1-5n)) * 4*16*(4^2)^(n-1) * 2.5 * 2.5^(11n-1)
------------------------------------------------------------------- =
160
(делим на 16 и делим на 10 (это) 4*2,5))
(5^(1-5n)) * (4^2)^(n-1) * 2.5^(11n-1)
=------------------------------------------------------------------- =
1
= (5^(1-5n)) * (4^2)^(n-1) * 2.5^(11n-1)