已知5的a次方=根号2,5的b次方=4次根号8求式子5的2a-2分之3b次方的值

2025-12-13 04:30:35
推荐回答(1个)
回答1:

2(⁴√2)/25
解:
5^a=√2
5^b=⁴√8
5^[3b/(2a-2)]
=5^(3b)/5^(2a-2)
=(5^b)^3/5^(2a-2)
=(5^b)^3/[5^(2a)*5^(-2)]
=(5^b)^3/[(5^a)²/25]
=[(⁴√8)^3]/(2/25)
=[2^(9/4)]/(2/25)
=(4*⁴√2)/(2/25)
=2(⁴√2)/25