Задача 79336 Упростите выражение [m]...

66f286c87e3eee7b6aef8ece

2/18/2025 1:58:00 PM

Упростите выражение

[m] N^{\frac{1}{\log_2 N}} \cdot N^{\frac{1}{\log_4 N}} \cdot N^{\frac{1}{\log_8 N}} \ldots N^{\frac{1}{\log_{512} N}} [/m]^{\frac{1}{15}}.

5f3eaa23faf909182968dde0

2/18/2025 4:15:23 PM

★

=(N^(log_(N)2)*N^(log_(N)4)*N^(log_(N)8*...*(N^(log_(N)512))))^(1/15)=
=(2*4*8*16*32*64*128*256*512)^(1/15)=
=(2^(1)*2^(2)*2^(3)*2^(4)*2^(5)*2^(6)*2^(7)*2^(8)*2^(9))^(1/15)=
=(2^(1+2+3+4+5+6+7+8+9))^(1/15)=(2^(45))^(1/15)=2^(45*(1/15))=2^(3)=8