数学题1/3×3×5(4的平方+1)(4的四次方+1)(4的八次方+1)+1/3等于多少？（要简便方法）
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解，原式=1/3*(4-1)*(4+1)*(4^2+1)*（4^4+1)*(4^8+1)+1/3
=1/3*(4^2-1)*(4^2+1)*（4^4+1)*(4^8+1)+1/3
=1/3*(4^4-1)*（4^4+1)*(4^8+1)+1/3
=1/3*(4^8-1)*(4^8+1)+1/3
=1/3*(4^16-1)+1/3
=1/3[(4^16-1)+1]
=4^16/3
=1/3*(4^2-1)*(4^2+1)*（4^4+1)*(4^8+1)+1/3
=1/3*(4^4-1)*（4^4+1)*(4^8+1)+1/3
=1/3*(4^8-1)*(4^8+1)+1/3
=1/3*(4^16-1)+1/3
=1/3[(4^16-1)+1]
=4^16/3
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(1/3)×3×5(4^2+1)(4^4+1)(4^8+1)+1/3
=(1/3)×(4-1)×(4+1)(4^2+1)(4^4+1)(4^8+1)+1/3
=(1/3)×(4^2-1)(4^2+1)(4^4+1)(4^8+1)+1/3
=(1/3)×(4^4-1)(4^4+1)(4^8+1)+1/3
=(1/3)×(4^8-1)(4^8+1)+1/3
=(1/3)×(4^16-1)+1/3
=(1/3)[(4^16-1)+1]
=(1/3)4^16
=(1/3)×(4-1)×(4+1)(4^2+1)(4^4+1)(4^8+1)+1/3
=(1/3)×(4^2-1)(4^2+1)(4^4+1)(4^8+1)+1/3
=(1/3)×(4^4-1)(4^4+1)(4^8+1)+1/3
=(1/3)×(4^8-1)(4^8+1)+1/3
=(1/3)×(4^16-1)+1/3
=(1/3)[(4^16-1)+1]
=(1/3)4^16
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